Acronym | tac | ||||||||||||||||||||
Name |
triacontiditeron, pentacross (β5), aeropet(id), pentachoral antiprism, vertex figure of gee, Gosset polytopes 21,1, lattice C5 contact polytope (span of its small roots), equatorial cross-section of vertex-first gee | ||||||||||||||||||||
Field of sections |
© | ||||||||||||||||||||
Circumradius | 1/sqrt(2) = 0.707107 | ||||||||||||||||||||
Inradius | 1/sqrt(10) = 0.316228 | ||||||||||||||||||||
Vertex figure |
© © | ||||||||||||||||||||
Lace city in approx. ASCII-art |
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o3o3o x3o3o o3o3x o3o3o | |||||||||||||||||||||
x o3o o x3o o o3x x o3o | |||||||||||||||||||||
Coordinates | (1/sqrt(2), 0, 0, 0, 0) & all permutations, all changes of sign | ||||||||||||||||||||
Volume | sqrt(2)/30 = 0.047140 | ||||||||||||||||||||
Surface | sqrt(5)/3 = 0.745356 | ||||||||||||||||||||
Rel. Roundness | 2 π2 sqrt(5)/125 = 35.310570 % | ||||||||||||||||||||
General of army | (is itself convex) | ||||||||||||||||||||
Colonel of regiment |
(is itself locally convex
– uniform polyteral members:
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Dual | pent | ||||||||||||||||||||
Dihedral angles | |||||||||||||||||||||
Face vector | 10, 40, 80, 80, 32 | ||||||||||||||||||||
Confer |
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External links |
Incidence matrix according to Dynkin symbol
x3o3o3o4o . . . . . | 10 ♦ 8 | 24 | 32 | 16 ----------+----+----+----+----+--- x . . . . | 2 | 40 ♦ 6 | 12 | 8 ----------+----+----+----+----+--- x3o . . . | 3 | 3 | 80 | 4 | 4 ----------+----+----+----+----+--- x3o3o . . ♦ 4 | 6 | 4 | 80 | 2 ----------+----+----+----+----+--- x3o3o3o . ♦ 5 | 10 | 10 | 5 | 32
x3o3o3o4/3o . . . . . | 10 ♦ 8 | 24 | 32 | 16 ------------+----+----+----+----+--- x . . . . | 2 | 40 ♦ 6 | 12 | 8 ------------+----+----+----+----+--- x3o . . . | 3 | 3 | 80 | 4 | 4 ------------+----+----+----+----+--- x3o3o . . ♦ 4 | 6 | 4 | 80 | 2 ------------+----+----+----+----+--- x3o3o3o . ♦ 5 | 10 | 10 | 5 | 32
o3o3o *b3o3x . . . . . | 10 ♦ 8 | 24 | 32 | 8 8 -------------+----+----+----+----+------ . . . . x | 2 | 40 ♦ 6 | 12 | 4 4 -------------+----+----+----+----+------ . . . o3x | 3 | 3 | 80 | 4 | 2 2 -------------+----+----+----+----+------ . o . *b3o3x ♦ 4 | 6 | 4 | 80 | 1 1 -------------+----+----+----+----+------ o3o . *b3o3x ♦ 5 | 10 | 10 | 5 | 16 * . o3o *b3o3x ♦ 5 | 10 | 10 | 5 | * 16
xo3oo3oo3ox&#x → height = sqrt(2/5) = 0.632456 (pen || dual pen) o.3o.3o.3o. | 5 * ♦ 4 4 0 | 6 12 6 0 | 4 12 12 4 0 | 1 4 6 4 1 0 .o3.o3.o3.o | * 5 ♦ 0 4 4 | 0 6 12 6 | 0 4 12 12 4 | 0 1 4 6 4 1 ---------------+-----+----------+-------------+--------------+-------------- x. .. .. .. | 2 0 | 10 * * ♦ 3 3 0 0 | 3 6 3 0 0 | 1 3 3 1 0 0 oo3oo3oo3oo&#x | 1 1 | * 20 * ♦ 0 3 3 0 | 0 3 6 3 0 | 0 1 3 3 1 0 .. .. .. .x | 0 2 | * * 10 ♦ 0 0 3 3 | 0 0 3 6 3 | 0 0 1 3 3 1 ---------------+-----+----------+-------------+--------------+-------------- x.3o. .. .. | 3 0 | 3 0 0 | 10 * * * | 2 2 0 0 0 | 1 2 1 0 0 0 xo .. .. ..&#x | 2 1 | 1 2 0 | * 30 * * | 0 2 2 0 0 | 0 1 2 1 0 0 .. .. .. ox&#x | 1 2 | 0 2 1 | * * 30 * | 0 0 2 2 0 | 0 0 1 2 1 0 .. .. .o3.x | 0 3 | 0 0 3 | * * * 10 | 0 0 0 2 2 | 0 0 0 1 2 1 ---------------+-----+----------+-------------+--------------+-------------- x.3o.3o. .. ♦ 4 0 | 6 0 0 | 4 0 0 0 | 5 * * * * | 1 1 0 0 0 0 xo3oo .. ..&#x ♦ 3 1 | 3 3 0 | 1 3 0 0 | * 20 * * * | 0 1 1 0 0 0 xo .. .. ox&#x ♦ 2 2 | 1 4 1 | 0 2 2 0 | * * 30 * * | 0 0 1 1 0 0 .. .. oo3ox&#x ♦ 1 3 | 0 3 3 | 0 0 3 1 | * * * 20 * | 0 0 0 1 1 0 .. .o3.o3.x ♦ 0 4 | 0 0 6 | 0 0 0 4 | * * * * 5 | 0 0 0 0 1 1 ---------------+-----+----------+-------------+--------------+-------------- x.3o.3o.3o. ♦ 5 0 | 10 0 0 | 10 0 0 0 | 5 0 0 0 0 | 1 * * * * * xo3oo3oo ..&#x ♦ 4 1 | 6 4 0 | 4 6 0 0 | 1 4 0 0 0 | * 5 * * * * xo3oo .. ox&#x ♦ 3 2 | 3 6 1 | 1 6 3 0 | 0 2 3 0 0 | * * 10 * * * xo .. oo3ox&#x ♦ 2 3 | 1 6 3 | 0 3 6 1 | 0 0 3 2 0 | * * * 10 * * .. oo3oo3ox&#x ♦ 1 4 | 0 4 6 | 0 0 6 4 | 0 0 0 4 1 | * * * * 5 * .o3.o3.o3.x ♦ 0 5 | 0 0 10 | 0 0 0 10 | 0 0 0 0 5 | * * * * * 1
or o.3o.3o.3o. & | 10 ♦ 4 4 | 6 18 | 4 16 12 | 1 5 10 -----------------+----+-------+-------+----------+-------- x. .. .. .. & | 2 | 20 * ♦ 3 3 | 3 6 3 | 1 3 4 oo3oo3oo3oo&#x | 2 | * 20 ♦ 0 6 | 0 6 6 | 0 2 6 -----------------+----+-------+-------+----------+-------- x.3o. .. .. & | 3 | 3 0 | 20 * | 2 2 0 | 1 2 1 xo .. .. ..&#x & | 3 | 1 2 | * 60 | 0 2 2 | 0 1 3 -----------------+----+-------+-------+----------+-------- x.3o.3o. .. & ♦ 4 | 6 0 | 4 0 | 10 * * | 1 1 0 xo3oo .. ..&#x & ♦ 4 | 3 3 | 1 3 | * 40 * | 0 1 1 xo .. .. ox&#x ♦ 4 | 2 4 | 0 4 | * * 30 | 0 0 2 -----------------+----+-------+-------+----------+-------- x.3o.3o.3o. & ♦ 5 | 10 0 | 10 0 | 5 0 0 | 2 * * xo3oo3oo ..&#x & ♦ 5 | 6 4 | 4 6 | 1 4 0 | * 10 * xo3oo .. ox&#x & ♦ 5 | 4 6 | 1 9 | 0 2 3 | * * 20
oxo3ooo3ooo4ooo&#xt → both heights = 1/sqrt(2) = 0.707107 (pt || pseudo hex || pt) o..3o..3o..4o.. | 1 * * ♦ 8 0 0 | 24 0 0 | 32 0 0 | 16 0 .o.3.o.3.o.4.o. | * 8 * ♦ 1 6 1 | 6 12 6 | 12 8 12 | 8 8 ..o3..o3..o4..o | * * 1 ♦ 0 0 8 | 0 0 24 | 0 0 32 | 0 16 -------------------+-------+--------+----------+----------+------ oo.3oo.3oo.4oo.&#x | 1 1 0 | 8 * * ♦ 6 0 0 | 12 0 0 | 8 0 .x. ... ... ... | 0 2 0 | * 24 * ♦ 1 4 1 | 4 4 4 | 4 4 .oo3.oo3.oo4.oo&#x | 0 1 1 | * * 8 ♦ 0 0 6 | 0 0 12 | 0 8 -------------------+-------+--------+----------+----------+------ ox. ... ... ...&#x | 1 2 0 | 2 1 0 | 24 * * | 4 0 0 | 4 0 .x.3.o. ... ... | 0 3 0 | 0 3 0 | * 32 * | 1 2 1 | 2 2 .xo ... ... ...&#x | 0 2 1 | 0 1 2 | * * 24 | 0 0 4 | 0 4 -------------------+-------+--------+----------+----------+------ ox.3oo. ... ...&#x ♦ 1 3 0 | 3 3 0 | 3 1 0 | 32 * * | 2 0 .x.3.o.3.o. ... ♦ 0 4 0 | 0 6 0 | 0 4 0 | * 16 * | 1 1 .xo3.oo ... ...&#x ♦ 0 3 1 | 0 3 3 | 0 1 3 | * * 32 | 0 2 -------------------+-------+--------+----------+----------+------ ox.3oo.3oo. ...&#x ♦ 1 4 0 | 4 6 0 | 6 4 0 | 4 1 0 | 16 * .xo3.oo3.oo ...&#x ♦ 0 4 1 | 0 6 4 | 0 4 6 | 0 1 4 | * 16
or o..3o..3o..4o.. & | 2 * ♦ 8 0 | 24 0 | 32 0 | 16 .o.3.o.3.o.4.o. | * 8 ♦ 2 6 | 12 12 | 24 8 | 16 ---------------------+-----+-------+-------+-------+--- oo.3oo.3oo.4oo.&#x & | 1 1 | 16 * ♦ 6 0 | 12 0 | 8 .x. ... ... ... | 0 2 | * 24 ♦ 2 4 | 8 4 | 8 ---------------------+-----+-------+-------+-------+--- ox. ... ... ...&#x & | 1 2 | 2 1 | 48 * | 4 0 | 4 .x.3.o. ... ... | 0 3 | 0 3 | * 32 | 2 2 | 4 ---------------------+-----+-------+-------+-------+--- ox.3oo. ... ...&#x & ♦ 1 3 | 3 3 | 3 1 | 64 * | 2 .x.3.o.3.o. ... ♦ 0 4 | 0 6 | 0 4 | * 16 | 2 ---------------------+-----+-------+-------+-------+--- ox.3oo.3oo. ...&#x & ♦ 1 4 | 4 6 | 6 4 | 4 1 | 32
qo ox3oo3oo4oo&#zx → height = 0 (tegum sum of q-line and perp hex) (tegum product of q-line with hex) o. o.3o.3o.4o. | 2 * ♦ 8 0 | 24 0 | 32 0 | 16 .o .o3.o3.o4.o | * 8 ♦ 2 6 | 12 12 | 24 8 | 16 ------------------+-----+-------+-------+-------+--- oo oo3oo3oo4oo&#x | 1 1 | 16 * ♦ 6 0 | 12 0 | 8 .. .x .. .. .. | 0 2 | * 24 ♦ 2 4 | 8 4 | 8 ------------------+-----+-------+-------+-------+--- .. ox .. .. ..&#x | 1 2 | 2 1 | 48 * | 4 0 | 4 .. .x3.o .. .. | 0 3 | 0 3 | * 32 | 2 2 | 4 ------------------+-----+-------+-------+-------+--- .. ox3oo .. ..&#x ♦ 1 3 | 3 3 | 3 1 | 64 * | 2 .. .x3.o3.o .. ♦ 0 4 | 0 6 | 0 4 | * 16 | 2 ------------------+-----+-------+-------+-------+--- .. ox3oo3oo ..&#x ♦ 1 4 | 4 6 | 6 4 | 4 1 | 32
oxo3ooo3ooo *b3ooo&#xt → both heights = 1/sqrt(2) = 0.707107 (pt || pseudo hex || pt) o..3o..3o.. *b3o.. | 1 * * ♦ 8 0 0 | 24 0 0 | 32 0 0 0 | 8 8 0 0 .o.3.o.3.o. *b3.o. | * 8 * ♦ 1 6 1 | 6 12 6 | 12 4 4 12 | 4 4 4 4 ..o3..o3..o *b3..o | * * 1 ♦ 0 0 8 | 0 0 24 | 0 0 0 32 | 0 0 8 8 ----------------------+-------+--------+----------+-----------+-------- oo.3oo.3oo. *b3oo.&#x | 1 1 0 | 8 * * ♦ 6 0 0 | 12 0 0 0 | 4 4 0 0 .x. ... ... ... | 0 2 0 | * 24 * ♦ 1 4 1 | 4 2 2 4 | 2 2 2 2 .oo3.oo3.oo *b3.oo&#x | 0 1 1 | * * 8 ♦ 0 0 6 | 0 0 0 12 | 0 0 4 4 ----------------------+-------+--------+----------+-----------+-------- ox. ... ... ...&#x | 1 2 0 | 2 1 0 | 24 * * | 4 0 0 0 | 2 2 0 0 .x.3.o. ... ... | 0 3 0 | 0 3 0 | * 32 * | 1 1 1 1 | 1 1 1 1 .xo ... ... ...&#x | 0 2 1 | 0 1 2 | * * 24 | 0 0 0 4 | 0 0 2 2 ----------------------+-------+--------+----------+-----------+-------- ox.3oo. ... ...&#x ♦ 1 3 0 | 3 3 0 | 3 1 0 | 32 * * * | 1 1 0 0 .x.3.o.3.o. ... ♦ 0 4 0 | 0 6 0 | 0 4 0 | * 8 * * | 1 0 1 0 .x.3.o. ... *b3.o. ♦ 0 4 0 | 0 6 0 | 0 4 0 | * * 8 * | 0 1 0 1 .xo3.oo ... ...&#x ♦ 0 3 1 | 0 3 3 | 0 1 3 | * * * 32 | 0 0 1 1 ----------------------+-------+--------+----------+-----------+-------- ox.3oo.3oo. ...&#x ♦ 1 4 0 | 4 6 0 | 6 4 0 | 4 1 0 0 | 8 * * * ox.3oo. ... *b3oo.&#x ♦ 1 4 0 | 4 6 0 | 6 4 0 | 4 0 1 0 | * 8 * * .xo3.oo3.oo ...&#x ♦ 0 4 1 | 0 6 4 | 0 4 6 | 0 1 0 4 | * * 8 * .xo3.oo ... *b3.oo&#x ♦ 0 4 1 | 0 6 4 | 0 4 6 | 0 0 1 4 | * * * 8
or o..3o..3o.. *b3o.. & | 2 * ♦ 8 0 | 24 0 | 32 0 0 | 8 8 .o.3.o.3.o. *b3.o. | * 8 ♦ 2 6 | 12 12 | 24 4 4 | 8 8 ------------------------+-----+-------+-------+--------+------ oo.3oo.3oo. *b3oo.&#x & | 1 1 | 16 * ♦ 6 0 | 12 0 0 | 4 4 .x. ... ... ... | 0 2 | * 24 ♦ 2 4 | 8 2 2 | 4 4 ------------------------+-----+-------+-------+--------+------ ox. ... ... ...&#x & | 1 2 | 2 1 | 48 * | 4 0 0 | 2 2 .x.3.o. ... ... | 0 3 | 0 3 | * 32 | 2 1 1 | 2 2 ------------------------+-----+-------+-------+--------+------ ox.3oo. ... ...&#x & ♦ 1 3 | 3 3 | 3 1 | 64 * * | 1 1 .x.3.o.3.o. ... ♦ 0 4 | 0 6 | 0 4 | * 8 * | 2 0 .x.3.o. ... *b3.o. ♦ 0 4 | 0 6 | 0 4 | * * 8 | 0 2 ------------------------+-----+-------+-------+--------+------ ox.3oo.3oo. ...&#x & ♦ 1 4 | 4 6 | 6 4 | 4 1 0 | 16 * ox.3oo. ... *b3oo.&#x & ♦ 1 4 | 4 6 | 6 4 | 4 0 1 | * 16
qo ox3oo3oo *b3oo&#zx → height = 0 (tegum sum of q-line and perp hex) (tegum product of q-line with hex) o. o.3o.3o. *b3o. | 2 * ♦ 8 0 | 24 0 | 32 0 0 | 8 8 .o .o3.o3.o *b3.o | * 8 ♦ 2 6 | 12 12 | 24 4 4 | 8 8 ---------------------+-----+-------+-------+--------+------ oo oo3oo3oo *b3oo&#x | 1 1 | 16 * ♦ 6 0 | 12 0 0 | 4 4 .. .x .. .. .. | 0 2 | * 24 ♦ 2 4 | 8 2 2 | 4 4 ---------------------+-----+-------+-------+--------+------ .. ox .. .. ..&#x | 1 2 | 2 1 | 48 * | 4 0 0 | 2 2 .. .x3.o .. .. | 0 3 | 0 3 | * 32 | 2 1 1 | 2 2 ---------------------+-----+-------+-------+--------+------ .. ox3oo .. ..&#x ♦ 1 3 | 3 3 | 3 1 | 64 * * | 1 1 .. .x3.o3.o .. ♦ 0 4 | 0 6 | 0 4 | * 8 * | 2 0 .. .x3.o .. *b3.o ♦ 0 4 | 0 6 | 0 4 | * * 8 | 0 2 ---------------------+-----+-------+-------+--------+------ .. ox3oo3oo ..&#x ♦ 1 4 | 4 6 | 6 4 | 4 1 0 | 16 * .. ox3oo .. *b3oo&#x ♦ 1 4 | 4 6 | 6 4 | 4 0 1 | * 16
xox oxo3ooo4ooo&#xt → both heights = 1/2 (line || perp pseudo oct || line) o.. o..3o..4o.. | 2 * * ♦ 1 6 1 0 0 0 | 6 12 6 0 0 0 | 12 8 12 0 0 | 8 8 0 .o. .o.3.o.4.o. | * 6 * ♦ 0 2 0 4 2 0 | 1 8 2 4 1 8 | 4 8 8 4 8 | 4 8 4 ..o ..o3..o4..o | * * 2 ♦ 0 0 1 0 6 1 | 0 0 6 0 6 12 | 0 0 12 12 8 | 0 8 8 -------------------+-------+----------------+----------------+----------------+------- x.. ... ... ... | 2 0 0 | 1 * * * * * ♦ 6 0 0 0 0 0 | 12 0 0 0 0 | 8 0 0 oo. oo.3oo.4oo.&#x | 1 1 0 | * 12 * * * * ♦ 1 4 1 0 0 0 | 4 4 4 0 0 | 4 4 0 o.o o.o3o.o4o.o&#x | 1 0 1 | * * 2 * * * ♦ 0 0 6 0 0 0 | 0 0 12 0 0 | 0 8 0 ... .x. ... ... | 0 2 0 | * * * 12 * * ♦ 0 2 0 2 0 2 | 1 4 2 1 4 | 2 4 2 .oo .oo3.oo4.oo&#x | 0 1 1 | * * * * 12 * ♦ 0 0 1 0 1 4 | 0 0 4 4 4 | 0 4 4 ..x ... ... ... | 0 0 2 | * * * * * 1 ♦ 0 0 0 0 6 0 | 0 0 0 12 0 | 0 0 8 -------------------+-------+----------------+----------------+----------------+------- xo. ... ... ...&#x | 2 1 0 | 1 2 0 0 0 0 | 6 * * * * * | 4 0 0 0 0 | 4 0 0 ... ox. ... ...&#x | 1 2 0 | 0 2 0 1 0 0 | * 24 * * * * | 1 2 1 0 0 | 2 2 0 ooo ooo3ooo4ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * 12 * * * | 0 0 4 0 0 | 0 4 0 ... .x.3.o. ... | 0 3 0 | 0 0 0 3 0 0 | * * * 8 * * | 0 2 0 0 2 | 1 2 1 .ox ... ... ...&#x | 0 1 2 | 0 0 0 0 2 1 | * * * * 6 * | 0 0 0 4 0 | 0 0 4 ... .xo ... ...&#x | 0 2 1 | 0 0 0 1 2 0 | * * * * * 24 | 0 0 1 1 2 | 0 2 2 -------------------+-------+----------------+----------------+----------------+------- xo. ox. ... ...&#x ♦ 2 2 0 | 1 4 0 1 0 0 | 2 2 0 0 0 0 | 12 * * * * | 2 0 0 ... ox.3oo. ...&#x ♦ 1 3 0 | 0 3 0 3 0 0 | 0 3 0 1 0 0 | * 16 * * * | 1 1 0 ... oxo ... ...&#x ♦ 1 2 1 | 0 2 1 1 2 0 | 0 1 2 0 0 1 | * * 24 * * | 0 2 0 .ox .xo ... ...&#x ♦ 0 2 2 | 0 0 0 1 4 1 | 0 0 0 0 2 2 | * * * 12 * | 0 0 2 ... .xo3.oo ...&#x ♦ 0 3 1 | 0 0 0 3 3 0 | 0 0 0 1 0 3 | * * * * 16 | 0 1 1 -------------------+-------+----------------+----------------+----------------+------- xo. ox.3oo. ...&#x ♦ 2 3 0 | 1 6 0 3 0 0 | 3 6 0 1 0 0 | 3 2 0 0 0 | 8 * * ... oxo3ooo ...&#x ♦ 1 3 1 | 0 3 1 3 3 0 | 0 3 3 1 0 3 | 0 1 3 0 1 | * 16 * .ox .xo3.oo ...&#x ♦ 0 3 2 | 0 0 0 3 6 1 | 0 0 0 1 3 6 | 0 0 0 3 2 | * * 8
or o.. o..3o..4o.. & | 4 * ♦ 1 6 1 0 | 6 12 6 0 | 12 8 12 | 8 8 .o. .o.3.o.4.o. | * 6 ♦ 0 4 0 4 | 2 16 2 4 | 8 16 8 | 8 8 ----------------------+-----+-----------+------------+----------+------ x.. ... ... ... & | 2 0 | 2 * * * ♦ 6 0 0 0 | 12 0 0 | 8 0 oo. oo.3oo.4oo.&#x & | 1 1 | * 24 * * ♦ 1 4 1 0 | 4 4 4 | 4 4 o.o o.o3o.o4o.o&#x | 2 0 | * * 2 * ♦ 0 0 6 0 | 0 0 12 | 0 8 ... .x. ... ... | 0 2 | * * * 12 ♦ 0 4 0 2 | 2 8 2 | 4 4 ----------------------+-----+-----------+------------+----------+------ xo. ... ... ...&#x & | 2 1 | 1 2 0 0 | 12 * * * | 4 0 0 | 4 0 ... ox. ... ...&#x & | 1 2 | 0 2 0 1 | * 48 * * | 1 2 1 | 2 2 ooo ooo3ooo4ooo&#x | 2 1 | 0 2 1 0 | * * 12 * | 0 0 4 | 0 4 ... .x.3.o. ... | 0 3 | 0 0 0 3 | * * * 8 | 0 4 0 | 2 2 ----------------------+-----+-----------+------------+----------+------ xo. ox. ... ...&#x & ♦ 2 2 | 1 4 0 1 | 2 2 0 0 | 24 * * | 2 0 ... ox.3oo. ...&#x & ♦ 1 3 | 0 3 0 3 | 0 3 0 1 | * 32 * | 1 1 ... oxo ... ...&#x ♦ 2 2 | 0 4 1 1 | 0 2 2 0 | * * 24 | 0 2 ----------------------+-----+-----------+------------+----------+------ xo. ox.3oo. ...&#x & ♦ 2 3 | 1 6 0 3 | 3 6 0 1 | 3 2 0 | 16 * ... oxo3ooo ...&#x ♦ 2 3 | 0 6 1 3 | 0 6 3 1 | 0 2 3 | * 16
xox ooo3oxo3ooo&#xt → both heights = 1/2 (line || perp pseudo oct || line) o.. o..3o..3o.. | 2 * * ♦ 1 6 1 0 0 0 | 6 12 6 0 0 0 0 | 12 4 4 12 0 0 0 | 4 4 4 4 0 0 .o. .o.3.o.3.o. | * 6 * ♦ 0 2 0 4 2 0 | 1 8 2 2 2 1 8 | 4 4 4 8 4 4 4 | 2 2 4 4 2 2 ..o ..o3..o3..o | * * 2 ♦ 0 0 1 0 6 1 | 0 0 6 0 0 6 12 | 0 0 0 12 12 4 4 | 0 0 4 4 4 4 -------------------+-------+----------------+------------------+------------------+------------ x.. ... ... ... | 2 0 0 | 1 * * * * * ♦ 6 0 0 0 0 0 0 | 12 0 0 0 0 0 0 | 4 4 0 0 0 0 oo. oo.3oo.3oo.&#x | 1 1 0 | * 12 * * * * ♦ 1 4 1 0 0 0 0 | 4 2 2 4 0 0 0 | 2 2 2 2 0 0 o.o o.o3o.o3o.o&#x | 1 0 1 | * * 2 * * * ♦ 0 0 6 0 0 0 0 | 0 0 0 12 0 0 0 | 0 0 4 4 0 0 ... ... .x. ... | 0 2 0 | * * * 12 * * ♦ 0 2 0 1 1 0 2 | 1 2 2 2 1 2 2 | 1 1 2 2 1 1 .oo .oo3.oo3.oo&#x | 0 1 1 | * * * * 12 * ♦ 0 0 1 0 0 1 4 | 0 0 0 4 4 2 2 | 0 0 2 2 2 2 ..x ... ... ... | 0 0 2 | * * * * * 1 ♦ 0 0 0 0 0 6 0 | 0 0 0 0 12 0 0 | 0 0 0 0 4 4 -------------------+-------+----------------+------------------+------------------+------------ xo. ... ... ...&#x | 2 1 0 | 1 2 0 0 0 0 | 6 * * * * * * | 4 0 0 0 0 0 0 | 2 2 0 0 0 0 ... ... ox. ...&#x | 1 2 0 | 0 2 0 1 0 0 | * 24 * * * * * | 1 1 1 1 0 0 0 | 1 1 1 1 0 0 ooo ooo3ooo3ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * 12 * * * * | 0 0 0 4 0 0 0 | 0 0 2 2 0 0 ... .o.3.x. ... | 0 3 0 | 0 0 0 3 0 0 | * * * 4 * * * | 0 2 0 0 0 2 0 | 1 0 2 0 1 0 ... ... .x.3.o. | 0 3 0 | 0 0 0 3 0 0 | * * * * 4 * * | 0 0 2 0 0 0 2 | 0 1 0 2 0 1 .ox ... ... ...&#x | 0 1 2 | 0 0 0 0 2 1 | * * * * * 6 * | 0 0 0 0 4 0 0 | 0 0 0 0 2 2 ... ... .xo ...&#x | 0 2 1 | 0 0 0 1 2 0 | * * * * * * 24 | 0 0 0 1 1 1 1 | 0 0 1 1 1 1 -------------------+-------+----------------+------------------+------------------+------------ xo. ... ox. ...&#x ♦ 2 2 0 | 1 4 0 1 0 0 | 2 2 0 0 0 0 0 | 12 * * * * * * | 1 1 0 0 0 0 ... oo.3ox. ...&#x ♦ 1 3 0 | 0 3 0 3 0 0 | 0 3 0 1 0 0 0 | * 8 * * * * * | 1 0 1 0 0 0 ... ... ox.3oo.&#x ♦ 1 3 0 | 0 3 0 3 0 0 | 0 3 0 0 1 0 0 | * * 8 * * * * | 0 1 0 1 0 0 ... ... oxo ...&#x ♦ 1 2 1 | 0 2 1 1 2 0 | 0 1 2 0 0 0 1 | * * * 24 * * * | 0 0 1 1 0 0 .ox ... .xo ...&#x ♦ 0 2 2 | 0 0 0 1 4 1 | 0 0 0 0 0 2 2 | * * * * 12 * * | 0 0 0 0 1 1 ... .oo3.xo ...&#x ♦ 0 3 1 | 0 0 0 3 3 0 | 0 0 0 1 0 0 3 | * * * * * 8 * | 0 0 1 0 1 0 ... ... .xo3.oo&#x ♦ 0 3 1 | 0 0 0 3 3 0 | 0 0 0 0 1 0 3 | * * * * * * 8 | 0 0 0 1 0 1 -------------------+-------+----------------+------------------+------------------+------------ xo. oo.3ox. ...&#x ♦ 2 3 0 | 1 6 0 3 0 0 | 3 6 0 1 0 0 0 | 3 2 0 0 0 0 0 | 4 * * * * * xo. ... ox.3oo.&#x ♦ 2 3 0 | 1 6 0 3 0 0 | 3 6 0 0 1 0 0 | 3 0 2 0 0 0 0 | * 4 * * * * ... ooo3oxo ...&#x ♦ 1 3 1 | 0 3 1 3 3 0 | 0 3 3 1 0 0 3 | 0 1 0 3 0 1 0 | * * 8 * * * ... ... oxo3ooo&#x ♦ 1 3 1 | 0 3 1 3 3 0 | 0 3 3 0 1 0 3 | 0 0 1 3 0 0 1 | * * * 8 * * .ox .oo3.xo ...&#x ♦ 0 3 2 | 0 0 0 3 6 1 | 0 0 0 1 0 3 6 | 0 0 0 0 3 2 0 | * * * * 4 * .ox ... .xo3.oo&#x ♦ 0 3 2 | 0 0 0 3 6 1 | 0 0 0 0 1 3 6 | 0 0 0 0 3 0 2 | * * * * * 4
or o.. o..3o..3o.. & | 4 * ♦ 1 6 1 0 | 6 12 6 0 0 | 12 4 4 12 | 4 4 4 4 .o. .o.3.o.3.o. | * 6 ♦ 0 4 0 4 | 2 16 2 2 2 | 8 8 8 8 | 4 4 4 4 ----------------------+-----+-----------+--------------+-------------+-------- x.. ... ... ... & | 2 0 | 2 * * * ♦ 6 0 0 0 0 | 12 0 0 0 | 4 4 0 0 oo. oo.3oo.3oo.&#x & | 1 1 | * 24 * * ♦ 1 4 1 0 0 | 4 2 2 4 | 2 2 2 2 o.o o.o3o.o3o.o&#x | 2 0 | * * 2 * ♦ 0 0 6 0 0 | 0 0 0 12 | 0 0 4 4 ... ... .x. ... | 0 2 | * * * 12 ♦ 0 4 0 1 1 | 2 4 4 2 | 2 2 2 2 ----------------------+-----+-----------+--------------+-------------+-------- xo. ... ... ...&#x & | 2 1 | 1 2 0 0 | 12 * * * * | 4 0 0 0 | 2 2 0 0 ... ... ox. ...&#x & | 1 2 | 0 2 0 1 | * 48 * * * | 1 1 1 1 | 1 1 1 1 ooo ooo3ooo3ooo&#x | 2 1 | 0 2 1 0 | * * 12 * * | 0 0 0 4 | 0 0 2 2 ... .o.3.x. ... | 0 3 | 0 0 0 3 | * * * 4 * | 0 4 0 0 | 2 0 2 0 ... ... .x.3.o. | 0 3 | 0 0 0 3 | * * * * 4 | 0 0 4 0 | 0 2 0 2 ----------------------+-----+-----------+--------------+-------------+-------- xo. ... ox. ...&#x & ♦ 2 2 | 1 4 0 1 | 2 2 0 0 0 | 24 * * * | 1 1 0 0 ... oo.3ox. ...&#x & ♦ 1 3 | 0 3 0 3 | 0 3 0 1 0 | * 16 * * | 1 0 1 0 ... ... ox.3oo.&#x & ♦ 1 3 | 0 3 0 3 | 0 3 0 0 1 | * * 16 * | 0 1 0 1 ... ... oxo ...&#x ♦ 2 2 | 0 4 1 1 | 0 2 2 0 0 | * * * 24 | 0 0 1 1 ----------------------+-----+-----------+--------------+-------------+-------- xo. oo.3ox. ...&#x & ♦ 2 3 | 1 6 0 3 | 3 6 0 1 0 | 3 2 0 0 | 8 * * * xo. ... ox.3oo.&#x & ♦ 2 3 | 1 6 0 3 | 3 6 0 0 1 | 3 0 2 0 | * 8 * * ... ooo3oxo ...&#x ♦ 2 3 | 0 6 1 3 | 0 6 3 1 0 | 0 2 0 3 | * * 8 * ... ... oxo3ooo&#x ♦ 2 3 | 0 6 1 3 | 0 6 3 0 1 | 0 0 2 3 | * * * 8
xoo3oox oxo4ooo&#xt → both heights = 1/sqrt(6) = 0.408248 ({3} || perp pseudo {4} || dual {3}) o..3o.. o..4o.. | 3 * * ♦ 2 4 2 0 0 0 | 1 8 4 2 1 8 0 0 0 | 4 8 8 4 8 0 0 | 4 8 4 0 .o.3.o. .o.4.o. | * 4 * ♦ 0 3 0 2 3 0 | 0 3 6 0 0 6 3 6 0 | 1 6 3 3 12 1 6 | 2 6 6 2 ..o3..o ..o4..o | * * 3 ♦ 0 0 2 0 4 2 | 0 0 0 1 2 8 8 4 1 | 0 0 4 8 8 4 8 | 0 4 8 4 -------------------+-------+---------------+------------------------+--------------------+---------- x.. ... ... ... | 2 0 0 | 3 * * * * * ♦ 1 4 0 1 0 0 0 0 0 | 4 4 4 0 0 0 0 | 4 4 0 0 oo.3oo. oo.4oo.&#x | 1 1 0 | * 12 * * * * ♦ 0 2 2 0 0 2 0 0 0 | 1 4 2 1 4 0 0 | 2 4 2 0 o.o3o.o o.o4o.o&#x | 1 0 1 | * * 6 * * * ♦ 0 0 0 1 1 4 0 0 0 | 0 0 4 4 4 0 0 | 0 4 4 0 ... ... .x. ... | 0 2 0 | * * * 4 * * ♦ 0 0 3 0 0 0 0 3 0 | 0 3 0 0 6 0 3 | 1 3 3 1 .oo3.oo .oo4.oo&#x | 0 1 1 | * * * * 12 * ♦ 0 0 0 0 0 2 2 2 0 | 0 0 1 2 4 1 4 | 0 2 4 2 ... ..x ... ... | 0 0 2 | * * * * * 3 ♦ 0 0 0 0 1 0 4 0 1 | 0 0 0 4 0 4 4 | 0 0 4 4 -------------------+-------+---------------+------------------------+--------------------+---------- x..3o.. ... ... | 3 0 0 | 3 0 0 0 0 0 | 1 * * * * * * * * | 4 0 0 0 0 0 0 | 4 0 0 0 xo. ... ... ...&#x | 2 1 0 | 1 2 0 0 0 0 | * 12 * * * * * * * | 1 2 1 0 0 0 0 | 2 2 0 0 ... ... ox. ...&#x | 1 2 0 | 0 2 0 1 0 0 | * * 12 * * * * * * | 0 2 0 0 2 0 0 | 1 2 1 0 x.o ... ... ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * * 3 * * * * * | 0 0 4 0 0 0 0 | 0 4 0 0 ... o.x ... ...&#x | 1 0 2 | 0 0 2 0 0 1 | * * * * 3 * * * * | 0 0 0 4 0 0 0 | 0 0 4 0 ooo3ooo ooo4ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * * 24 * * * | 0 0 1 1 2 0 0 | 0 2 2 0 ... .ox ... ...&#x | 0 1 2 | 0 0 0 0 2 1 | * * * * * * 12 * * | 0 0 0 1 0 1 2 | 0 0 2 2 ... ... .xo ...&#x | 0 2 1 | 0 0 0 1 2 0 | * * * * * * * 12 * | 0 0 0 0 2 0 2 | 0 1 2 1 ..o3..x ... ... | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * 1 | 0 0 0 0 0 4 0 | 0 0 0 4 -------------------+-------+---------------+------------------------+--------------------+---------- xo.3oo. ... ...&#x ♦ 3 1 0 | 3 3 0 0 0 0 | 1 3 0 0 0 0 0 0 0 | 4 * * * * * * | 2 0 0 0 xo. ... ox. ...&#x ♦ 2 2 0 | 1 4 0 1 0 0 | 0 2 2 0 0 0 0 0 0 | * 12 * * * * * | 1 1 0 0 xoo ... ... ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 0 1 0 1 0 2 0 0 0 | * * 12 * * * * | 0 2 0 0 ... oox ... ...&#x ♦ 1 1 2 | 0 1 2 0 2 1 | 0 0 0 0 1 2 1 0 0 | * * * 12 * * * | 0 0 2 0 ... ... oxo ...&#x ♦ 1 2 1 | 0 2 1 1 2 0 | 0 0 1 0 0 2 0 1 0 | * * * * 24 * * | 0 1 1 0 .oo3.ox ... ...&#x ♦ 0 1 3 | 0 0 0 0 3 3 | 0 0 0 0 0 0 3 0 1 | * * * * * 4 * | 0 0 0 2 ... .ox .xo ...&#x ♦ 0 2 2 | 0 0 0 1 4 1 | 0 0 0 0 0 0 2 2 0 | * * * * * * 12 | 0 0 1 1 -------------------+-------+---------------+------------------------+--------------------+---------- xo.3oo. ox. ...&#x ♦ 3 2 0 | 3 6 0 1 0 0 | 1 6 3 0 0 0 0 0 0 | 2 3 0 0 0 0 0 | 4 * * * xoo ... oxo ...&#x ♦ 2 2 1 | 1 4 2 1 2 0 | 0 2 2 1 0 4 0 1 0 | 0 1 2 0 2 0 0 | * 12 * * ... oox oxo ...&#x ♦ 1 2 2 | 0 2 2 1 4 1 | 0 0 1 0 1 4 2 2 0 | 0 0 0 2 2 0 1 | * * 12 * .oo3.ox .xo ...&#x ♦ 0 2 3 | 0 0 0 1 6 3 | 0 0 0 0 0 0 6 3 1 | 0 0 0 0 0 2 3 | * * * 4
or o..3o.. o..4o.. & | 6 * ♦ 2 4 2 0 | 1 8 4 3 8 | 4 8 12 8 | 4 12 .o.3.o. .o.4.o. | * 4 ♦ 0 6 0 2 | 0 6 12 0 6 | 2 12 6 12 | 4 12 ---------------------+-----+----------+--------------+------------+----- x.. ... ... ... & | 2 0 | 6 * * * ♦ 1 4 0 1 0 | 4 4 4 0 | 4 4 oo.3oo. oo.4oo.&#x & | 1 1 | * 24 * * ♦ 0 2 2 0 2 | 1 4 3 4 | 2 6 o.o3o.o o.o4o.o&#x | 2 0 | * * 6 * ♦ 0 0 0 2 4 | 0 0 8 4 | 0 8 ... ... .x. ... | 0 2 | * * * 4 ♦ 0 0 6 0 0 | 0 6 0 6 | 2 6 ---------------------+-----+----------+--------------+------------+----- x..3o.. ... ... & | 3 0 | 3 0 0 0 | 2 * * * * | 4 0 0 0 | 4 0 xo. ... ... ...&#x & | 2 1 | 1 2 0 0 | * 24 * * * | 1 2 1 0 | 2 2 ... ... ox. ...&#x & | 1 2 | 0 2 0 1 | * * 24 * * | 0 2 0 2 | 1 3 x.o ... ... ...&#x & | 3 0 | 1 0 2 0 | * * * 6 * | 0 0 4 0 | 0 4 ooo3ooo ooo4ooo&#x | 2 1 | 0 2 1 0 | * * * * 24 | 0 0 2 2 | 0 4 ---------------------+-----+----------+--------------+------------+----- xo.3oo. ... ...&#x & ♦ 3 1 | 3 3 0 0 | 1 3 0 0 0 | 8 * * * | 2 0 xo. ... ox. ...&#x & ♦ 2 2 | 1 4 0 1 | 0 2 2 0 0 | * 24 * * | 1 1 xoo ... ... ...&#x & ♦ 3 1 | 1 3 2 0 | 0 1 0 1 2 | * * 24 * | 0 2 ... ... oxo ...&#x ♦ 2 2 | 0 4 1 1 | 0 0 2 0 2 | * * * 24 | 0 2 ---------------------+-----+----------+--------------+------------+----- xo.3oo. ox. ...&#x & ♦ 3 2 | 3 6 0 1 | 1 6 3 0 0 | 2 3 0 0 | 8 * xoo ... oxo ...&#x & ♦ 3 2 | 1 6 2 1 | 0 2 3 1 4 | 0 1 2 2 | * 24
oxo oxo xoo3oox&#xt → both heights = 1/sqrt(6) = 0.408248 ({3} || perp pseudo {4} || dual {3}) o.. o.. o..3o.. | 3 * * ♦ 2 4 2 0 0 0 0 | 1 2 2 8 2 1 8 0 0 0 0 | 4 4 4 4 4 8 4 0 0 0 | 2 2 4 2 4 2 0 0 .o. .o. .o.3.o. | * 4 * ♦ 0 3 0 1 1 3 0 | 0 3 3 3 0 0 6 3 3 3 0 | 3 3 1 6 6 3 3 3 3 1 | 1 1 3 3 3 3 1 1 ..o ..o ..o3..o | * * 3 ♦ 0 0 2 0 0 4 2 | 0 0 0 0 1 2 8 2 2 8 1 | 0 0 0 4 4 4 8 4 4 4 | 0 0 2 4 2 4 2 2 -------------------+-------+-----------------+--------------------------+-------------------------+---------------- ... ... x.. ... | 2 0 0 | 3 * * * * * * ♦ 1 0 0 4 1 0 0 0 0 0 0 | 2 2 4 0 0 4 0 0 0 0 | 2 2 2 0 2 0 0 0 oo. oo. oo.3oo.&#x | 1 1 0 | * 12 * * * * * ♦ 0 1 1 2 0 0 2 0 0 0 0 | 2 2 1 2 2 2 1 0 0 0 | 1 1 2 1 2 1 0 0 o.o o.o o.o3o.o&#x | 1 0 1 | * * 6 * * * * ♦ 0 0 0 0 1 1 4 0 0 0 0 | 0 0 0 2 2 4 4 0 0 0 | 0 0 2 2 2 2 0 0 .x. ... ... ... | 0 2 0 | * * * 2 * * * ♦ 0 3 0 0 0 0 0 3 0 0 0 | 3 0 0 6 0 0 0 3 0 0 | 1 0 3 3 0 0 1 0 ... .x. ... ... | 0 2 0 | * * * * 2 * * ♦ 0 0 3 0 0 0 0 0 3 0 0 | 0 3 0 0 6 0 0 0 3 0 | 0 1 0 0 3 3 0 1 .oo .oo .oo3.oo&#x | 0 1 1 | * * * * * 12 * ♦ 0 0 0 0 0 0 2 1 1 2 0 | 0 0 0 2 2 1 2 2 2 1 | 0 0 1 2 1 2 1 1 ... ... ... ..x | 0 0 2 | * * * * * * 3 ♦ 0 0 0 0 0 1 0 0 0 4 1 | 0 0 0 0 0 0 4 2 2 4 | 0 0 0 2 0 2 2 2 -------------------+-------+-----------------+--------------------------+-------------------------+---------------- ... ... x..3o.. | 3 0 0 | 3 0 0 0 0 0 0 | 1 * * * * * * * * * * | 0 0 4 0 0 0 0 0 0 0 | 2 2 0 0 0 0 0 0 ox. ... ... ...&#x | 1 2 0 | 0 2 0 1 0 0 0 | * 6 * * * * * * * * * | 2 0 0 2 0 0 0 0 0 0 | 1 0 2 1 0 0 0 0 ... ox. ... ...&#x | 1 2 0 | 0 2 0 0 1 0 0 | * * 6 * * * * * * * * | 0 2 0 0 2 0 0 0 0 0 | 0 1 0 0 2 1 0 0 ... ... xo. ...&#x | 2 1 0 | 1 2 0 0 0 0 0 | * * * 12 * * * * * * * | 1 1 1 0 0 1 0 0 0 0 | 1 1 1 0 1 0 0 0 ... ... x.o ...&#x | 2 0 1 | 1 0 2 0 0 0 0 | * * * * 3 * * * * * * | 0 0 0 0 0 4 0 0 0 0 | 0 0 2 0 2 0 0 0 ... ... ... o.x&#x | 1 0 2 | 0 0 2 0 0 0 1 | * * * * * 3 * * * * * | 0 0 0 0 0 0 4 0 0 0 | 0 0 0 2 0 2 0 0 ooo ooo ooo3ooo&#x | 1 1 1 | 0 1 1 0 0 1 0 | * * * * * * 24 * * * * | 0 0 0 1 1 1 1 0 0 0 | 0 0 1 1 1 1 0 0 .xo ... ... ...&#x | 0 2 1 | 0 0 0 1 0 2 0 | * * * * * * * 6 * * * | 0 0 0 2 0 0 0 2 0 0 | 0 0 1 2 0 0 1 0 ... .xo ... ...&#x | 0 2 1 | 0 0 0 0 1 2 0 | * * * * * * * * 6 * * | 0 0 0 0 2 0 0 0 2 0 | 0 0 0 0 1 2 0 1 ... ... ... .ox&#x | 0 1 2 | 0 0 0 0 0 2 1 | * * * * * * * * * 12 * | 0 0 0 0 0 0 1 1 1 1 | 0 0 0 1 0 1 1 1 ... ... ..o3..x | 0 0 3 | 0 0 0 0 0 0 3 | * * * * * * * * * * 1 | 0 0 0 0 0 0 0 0 0 4 | 0 0 0 0 0 0 2 2 -------------------+-------+-----------------+--------------------------+-------------------------+---------------- ox. ... xo. ...&#x ♦ 2 2 0 | 1 4 0 1 0 0 0 | 0 2 0 2 0 0 0 0 0 0 0 | 6 * * * * * * * * * | 1 0 1 0 0 0 0 0 ... ox. xo. ...&#x ♦ 2 2 0 | 1 4 0 0 1 0 0 | 0 0 2 2 0 0 0 0 0 0 0 | * 6 * * * * * * * * | 0 1 0 0 1 0 0 0 ... ... xo.3oo.&#x ♦ 3 1 0 | 3 3 0 0 0 0 0 | 1 0 0 3 0 0 0 0 0 0 0 | * * 4 * * * * * * * | 1 1 0 0 0 0 0 0 oxo ... ... ...&#x ♦ 1 2 1 | 0 2 1 1 0 2 0 | 0 1 0 0 0 0 2 1 0 0 0 | * * * 12 * * * * * * | 0 0 1 1 0 0 0 0 ... oxo ... ...&#x ♦ 1 2 1 | 0 2 1 0 1 2 0 | 0 0 1 0 0 0 2 0 1 0 0 | * * * * 12 * * * * * | 0 0 0 0 1 1 0 0 ... ... xoo ...&#x ♦ 2 1 1 | 1 2 2 0 0 1 0 | 0 0 0 1 1 0 2 0 0 0 0 | * * * * * 12 * * * * | 0 0 1 0 1 0 0 0 ... ... ... oox&#x ♦ 1 1 2 | 0 1 2 0 0 2 1 | 0 0 0 0 0 1 2 0 0 1 0 | * * * * * * 12 * * * | 0 0 0 1 0 1 0 0 .xo ... ... .ox&#x ♦ 0 2 2 | 0 0 0 1 0 4 1 | 0 0 0 0 0 0 0 2 0 2 0 | * * * * * * * 6 * * | 0 0 0 1 0 0 1 0 ... .xo ... .ox&#x ♦ 0 2 2 | 0 0 0 0 1 4 1 | 0 0 0 0 0 0 0 0 2 2 0 | * * * * * * * * 6 * | 0 0 0 0 0 1 0 1 ... ... .oo3.ox&#x ♦ 0 1 3 | 0 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 0 3 1 | * * * * * * * * * 4 | 0 0 0 0 0 0 1 1 -------------------+-------+-----------------+--------------------------+-------------------------+---------------- ox. ... xo.3oo.&#x ♦ 3 2 0 | 3 6 0 1 0 0 0 | 1 3 0 6 0 0 0 0 0 0 0 | 3 0 2 0 0 0 0 0 0 0 | 2 * * * * * * * ... ox. xo.3oo.&#x ♦ 3 2 0 | 3 6 0 0 1 0 0 | 1 0 3 6 0 0 0 0 0 0 0 | 0 3 2 0 0 0 0 0 0 0 | * 2 * * * * * * oxo ... xoo ...&#x ♦ 2 2 1 | 1 4 2 1 0 2 0 | 0 2 0 2 1 0 4 1 0 0 0 | 1 0 0 2 0 2 0 0 0 0 | * * 6 * * * * * oxo ... ... oox&#x ♦ 1 2 2 | 0 2 2 1 0 4 1 | 0 1 0 0 0 1 4 2 0 2 0 | 0 0 0 2 0 0 2 1 0 0 | * * * 6 * * * * ... oxo xoo ...&#x ♦ 2 2 1 | 1 4 2 0 1 2 0 | 0 0 2 2 1 0 4 0 1 0 0 | 0 1 0 0 2 2 0 0 0 0 | * * * * 6 * * * ... oxo ... oox&#x ♦ 1 2 2 | 0 2 2 0 1 4 1 | 0 0 1 0 0 1 4 0 2 2 0 | 0 0 0 0 2 0 2 0 1 0 | * * * * * 6 * * .xo ... .oo3.ox&#x ♦ 0 2 3 | 0 0 0 1 0 6 3 | 0 0 0 0 0 0 0 3 0 6 1 | 0 0 0 0 0 0 0 3 0 2 | * * * * * * 2 * ... .xo .oo3.ox&#x ♦ 0 2 3 | 0 0 0 0 1 6 3 | 0 0 0 0 0 0 0 0 3 6 1 | 0 0 0 0 0 0 0 0 3 2 | * * * * * * * 2
or o.. o.. o..3o.. & | 6 * ♦ 2 4 2 0 0 | 1 2 2 8 3 8 | 4 4 4 4 4 12 | 2 2 6 6 .o. .o. .o.3.o. | * 4 ♦ 0 6 0 1 1 | 0 6 6 6 0 6 | 6 6 2 6 6 6 | 2 2 6 6 ---------------------+-----+------------+-----------------+------------------+---------- ... ... x.. ... & | 2 0 | 6 * * * * ♦ 1 0 0 4 1 0 | 2 2 4 0 0 4 | 2 2 2 2 oo. oo. oo.3oo.&#x & | 1 1 | * 24 * * * ♦ 0 1 1 2 0 2 | 2 2 1 2 2 3 | 1 1 3 3 o.o o.o o.o3o.o&#x | 2 0 | * * 6 * * ♦ 0 0 0 0 2 4 | 0 0 0 2 2 8 | 0 0 4 4 .x. ... ... ... | 0 2 | * * * 2 * ♦ 0 6 0 0 0 0 | 6 0 0 6 0 0 | 2 0 6 0 ... .x. ... ... | 0 2 | * * * * 2 ♦ 0 0 6 0 0 0 | 0 6 0 0 6 0 | 0 2 0 6 ---------------------+-----+------------+-----------------+------------------+---------- ... ... x..3o.. & | 3 0 | 3 0 0 0 0 | 2 * * * * * | 0 0 4 0 0 0 | 2 2 0 0 ox. ... ... ...&#x & | 1 2 | 0 2 0 1 0 | * 12 * * * * | 2 0 0 2 0 0 | 1 0 3 0 ... ox. ... ...&#x & | 1 2 | 0 2 0 0 1 | * * 12 * * * | 0 2 0 0 2 0 | 0 1 0 3 ... ... xo. ...&#x & | 2 1 | 1 2 0 0 0 | * * * 24 * * | 1 1 1 0 0 1 | 1 1 1 1 ... ... x.o ...&#x & | 3 0 | 1 0 2 0 0 | * * * * 6 * | 0 0 0 0 0 4 | 0 0 2 2 ooo ooo ooo3ooo&#x | 2 1 | 0 2 1 0 0 | * * * * * 24 | 0 0 0 1 1 2 | 0 0 2 2 ---------------------+-----+------------+-----------------+------------------+---------- ox. ... xo. ...&#x & ♦ 2 2 | 1 4 0 1 0 | 0 2 0 2 0 0 | 12 * * * * * | 1 0 1 0 ... ox. xo. ...&#x & ♦ 2 2 | 1 4 0 0 1 | 0 0 2 2 0 0 | * 12 * * * * | 0 1 0 1 ... ... xo.3oo.&#x & ♦ 3 1 | 3 3 0 0 0 | 1 0 0 3 0 0 | * * 8 * * * | 1 1 0 0 oxo ... ... ...&#x ♦ 2 2 | 0 4 1 1 0 | 0 2 0 0 0 2 | * * * 12 * * | 0 0 2 0 ... oxo ... ...&#x ♦ 2 2 | 0 4 1 0 1 | 0 0 2 0 0 2 | * * * * 12 * | 0 0 0 2 ... ... xoo ...&#x & ♦ 3 1 | 1 3 2 0 0 | 0 0 0 1 1 2 | * * * * * 24 | 0 0 1 1 ---------------------+-----+------------+-----------------+------------------+---------- ox. ... xo.3oo.&#x & ♦ 3 2 | 3 6 0 1 0 | 1 3 0 6 0 0 | 3 0 2 0 0 0 | 4 * * * ... ox. xo.3oo.&#x & ♦ 3 2 | 3 6 0 0 1 | 1 0 3 6 0 0 | 0 3 2 0 0 0 | * 4 * * oxo ... xoo ...&#x & ♦ 3 2 | 1 6 2 1 0 | 0 3 0 2 1 4 | 1 0 0 2 0 2 | * * 12 * ... oxo xoo ...&#x & ♦ 3 2 | 1 6 2 0 1 | 0 0 3 2 1 4 | 0 1 0 0 2 2 | * * * 12
ox4oo xo3oo4oo&#zx → height = 0 (tegum sum of oct and perp {4}) o.4o. o.3o.4o. | 6 * ♦ 4 4 0 | 4 4 16 | 16 16 | 16 .o4.o .o3.o4.o | * 4 ♦ 0 6 2 | 0 12 12 | 24 8 | 16 -------------------+-----+---------+---------+-------+--- .. .. x. .. .. | 2 0 | 12 * * ♦ 2 0 4 | 4 8 | 8 oo4oo oo3oo4oo&#x | 1 1 | * 24 * ♦ 0 2 4 | 8 4 | 8 .x .. .. .. .. | 0 2 | * * 4 ♦ 0 6 0 | 12 0 | 8 -------------------+-----+---------+---------+-------+--- .. .. x.3o. .. | 3 0 | 3 0 0 | 8 * * | 0 4 | 4 ox .. .. .. ..&#x | 1 2 | 0 2 1 | * 24 * | 4 0 | 4 .. .. xo .. ..&#x | 2 1 | 1 2 0 | * * 48 | 2 2 | 4 -------------------+-----+---------+---------+-------+--- ox .. xo .. ..&#x ♦ 2 2 | 1 4 1 | 0 2 2 | 48 * | 2 .. .. xo3oo ..&#x ♦ 3 1 | 3 3 0 | 1 0 3 | * 32 | 2 -------------------+-----+---------+---------+-------+--- ox .. xo3oo ..&#x ♦ 3 2 | 3 6 1 | 1 3 6 | 3 2 | 32
xoo3ooo3oox oqo&#xt → both heights = 1/sqrt(8) = 0.353553 (tet || pseudo perp q-line || dual tet) o..3o..3o.. o.. | 4 * * ♦ 3 2 3 0 0 | 3 6 6 3 6 0 0 | 1 6 3 3 1 12 6 0 0 | 2 6 6 2 0 .o.3.o.3.o. .o. | * 2 * ♦ 0 4 0 4 0 | 0 6 0 0 12 6 0 | 0 4 0 0 0 12 12 4 0 | 1 4 6 4 1 ..o3..o3..o ..o | * * 4 ♦ 0 0 3 2 3 | 0 0 3 6 6 6 3 | 0 0 1 3 3 6 12 6 1 | 0 2 6 6 2 --------------------+-------+------------+--------------------+---------------------+----------- x.. ... ... ... | 2 0 0 | 6 * * * * ♦ 2 2 2 0 0 0 0 | 1 4 2 1 0 4 0 0 0 | 2 4 2 0 0 oo.3oo.3oo. oo.&#x | 1 1 0 | * 8 * * * ♦ 0 3 0 0 3 0 0 | 0 3 0 0 0 6 3 0 0 | 1 3 3 1 0 o.o3o.o3o.o o.o&#x | 1 0 1 | * * 12 * * ♦ 0 0 2 2 2 0 0 | 0 0 1 2 1 4 4 0 0 | 0 2 4 2 0 .oo3.oo3.oo .oo&#x | 0 1 1 | * * * 8 * ♦ 0 0 0 0 3 3 0 | 0 0 0 0 0 3 6 3 0 | 0 1 3 3 1 ... ... ..x ... | 0 0 2 | * * * * 6 ♦ 0 0 0 2 0 2 2 | 0 0 0 1 2 0 4 4 1 | 0 0 2 4 2 --------------------+-------+------------+--------------------+---------------------+----------- x..3o.. ... ... | 3 0 0 | 3 0 0 0 0 | 4 * * * * * * | 1 2 1 0 0 0 0 0 0 | 2 2 0 0 0 xo. ... ... ...&#x | 2 1 0 | 1 2 0 0 0 | * 12 * * * * * | 0 2 0 0 0 2 0 0 0 | 1 2 1 0 0 x.o ... ... ...&#x | 2 0 1 | 1 0 2 0 0 | * * 12 * * * * | 0 0 1 1 0 2 0 0 0 | 0 2 2 0 0 ... ... o.x ...&#x | 1 0 2 | 0 0 2 0 1 | * * * 12 * * * | 0 0 0 1 1 0 2 0 0 | 0 0 2 2 0 ooo3ooo3ooo ooo&#x | 1 1 1 | 0 1 1 1 0 | * * * * 24 * * | 0 0 0 0 0 2 2 0 0 | 0 1 2 1 0 ... ... .ox ...&#x | 0 1 2 | 0 0 0 2 1 | * * * * * 12 * | 0 0 0 0 0 0 2 2 0 | 0 0 1 2 1 ... ..o3..x ... | 0 0 3 | 0 0 0 0 3 | * * * * * * 4 | 0 0 0 0 1 0 0 2 1 | 0 0 0 2 2 --------------------+-------+------------+--------------------+---------------------+----------- x..3o..3o.. ... ♦ 4 0 0 | 6 0 0 0 0 | 4 0 0 0 0 0 0 | 1 * * * * * * * * | 2 0 0 0 0 xo.3oo. ... ...&#x ♦ 3 1 0 | 3 3 0 0 0 | 1 3 0 0 0 0 0 | * 8 * * * * * * * | 1 1 0 0 0 x.o3o.o ... ...&#x ♦ 3 0 1 | 3 0 3 0 0 | 1 0 3 0 0 0 0 | * * 4 * * * * * * | 0 2 0 0 0 x.o ... o.x ...&#x ♦ 2 0 2 | 1 0 4 0 1 | 0 0 2 2 0 0 0 | * * * 6 * * * * * | 0 0 2 0 0 ... o.o3o.x ...&#x ♦ 1 0 3 | 0 0 3 0 3 | 0 0 0 3 0 0 1 | * * * * 4 * * * * | 0 0 0 2 0 xoo ... ... ...&#x ♦ 2 1 1 | 1 2 2 1 0 | 0 1 1 0 2 0 0 | * * * * * 24 * * * | 0 1 1 0 0 ... ... oox ...&#x ♦ 1 1 2 | 0 1 2 2 1 | 0 0 0 1 2 1 0 | * * * * * * 24 * * | 0 0 1 1 0 ... .oo3.ox ...&#x ♦ 0 1 3 | 0 0 0 3 3 | 0 0 0 0 0 3 1 | * * * * * * * 8 * | 0 0 0 1 1 ..o3..o3..x ... ♦ 0 0 4 | 0 0 0 0 6 | 0 0 0 0 0 0 4 | * * * * * * * * 1 | 0 0 0 0 2 --------------------+-------+------------+--------------------+---------------------+----------- xo.3oo.3oo. ...&#x ♦ 4 1 0 | 6 4 0 0 0 | 4 6 0 0 0 0 0 | 1 4 0 0 0 0 0 0 0 | 2 * * * * xoo3ooo ... ...&#x ♦ 3 1 1 | 3 3 3 1 0 | 1 3 3 0 3 0 0 | 0 1 1 0 0 3 0 0 0 | * 8 * * * xoo ... oox ...&#x ♦ 2 1 2 | 1 2 4 2 1 | 0 1 2 2 4 1 0 | 0 0 0 1 0 2 2 0 0 | * * 12 * * ... ooo3oox ...&#x ♦ 1 1 3 | 0 1 3 3 3 | 0 0 0 3 3 3 1 | 0 0 0 0 1 0 3 1 0 | * * * 8 * .oo3.oo3.ox ...&#x ♦ 0 1 4 | 0 0 0 4 6 | 0 0 0 0 0 6 4 | 0 0 0 0 0 0 0 4 1 | * * * * 2
oxoo3oooo3ooox&#xr → all cyclical heights = sqrt(5/8) = 0.790569 in fact a rhomb with diagonals height(1,3) = sqrt(2) = 1.414214 height(2,4) = 1/sqrt(2) = 0.707107 o...3o...3o... | 1 * * * ♦ 4 4 0 0 0 0 0 | 6 6 12 0 0 0 0 0 0 0 | 4 4 12 12 0 0 0 0 0 0 0 0 0 | 1 1 4 6 4 0 0 0 0 0 .o..3.o..3.o.. | * 4 * * ♦ 1 0 3 1 3 0 0 | 3 0 3 3 3 6 3 3 0 0 | 3 0 6 3 1 3 3 3 1 6 3 0 0 | 1 0 3 3 1 1 3 3 1 0 ..o.3..o.3..o. | * * 1 * ♦ 0 0 0 4 0 4 0 | 0 0 0 0 6 0 0 12 6 0 | 0 0 0 0 0 4 0 0 0 12 12 4 0 | 0 0 0 0 0 1 4 6 4 1 ...o3...o3...o | * * * 4 ♦ 0 1 0 0 3 1 3 | 0 3 3 0 0 3 6 3 3 3 | 0 3 3 6 0 0 1 3 3 3 6 3 1 | 0 1 1 3 3 0 1 3 3 1 ------------------+---------+----------------+-------------------------+-------------------------------+-------------------- oo..3oo..3oo..&#x | 1 1 0 0 | 4 * * * * * * ♦ 3 0 3 0 0 0 0 0 0 0 | 3 0 6 3 0 0 0 0 0 0 0 0 0 | 1 0 3 3 1 0 0 0 0 0 o..o3o..o3o..o&#x | 1 0 0 1 | * 4 * * * * * ♦ 0 3 3 0 0 0 0 0 0 0 | 0 3 3 6 0 0 0 0 0 0 0 0 0 | 0 1 1 3 3 0 0 0 0 0 .x.. .... .... | 0 2 0 0 | * * 6 * * * * ♦ 1 0 0 2 1 2 0 0 0 0 | 2 0 2 0 1 2 2 1 0 2 0 0 0 | 1 0 2 1 0 1 2 1 0 0 .oo.3.oo.3.oo.&#x | 0 1 1 0 | * * * 4 * * * ♦ 0 0 0 0 3 0 0 3 0 0 | 0 0 0 0 0 3 0 0 0 6 3 0 0 | 0 0 0 0 0 1 3 3 1 0 .o.o3.o.o3.o.o&#x | 0 1 0 1 | * * * * 12 * * ♦ 0 0 1 0 0 2 2 1 0 0 | 0 0 2 2 0 0 1 2 1 2 2 0 0 | 0 0 1 2 1 0 1 2 1 0 ..oo3..oo3..oo&#x | 0 0 1 1 | * * * * * 4 * ♦ 0 0 0 0 0 0 0 3 3 0 | 0 0 0 0 0 0 0 0 0 3 6 3 0 | 0 0 0 0 0 0 1 3 3 1 .... .... ...x | 0 0 0 2 | * * * * * * 6 ♦ 0 1 0 0 0 0 2 0 1 2 | 0 2 0 2 0 0 0 1 2 0 2 2 1 | 0 1 0 1 2 0 0 1 2 1 ------------------+---------+----------------+-------------------------+-------------------------------+-------------------- ox.. .... ....&#x | 1 2 0 0 | 2 0 1 0 0 0 0 | 6 * * * * * * * * * | 2 0 2 0 0 0 0 0 0 0 0 0 0 | 1 0 2 1 0 0 0 0 0 0 .... .... o..x&#x | 1 0 0 2 | 0 2 0 0 0 0 1 | * 6 * * * * * * * * | 0 2 0 2 0 0 0 0 0 0 0 0 0 | 0 1 0 1 2 0 0 0 0 0 oo.o3oo.o3oo.o&#x | 1 1 0 1 | 1 1 0 0 1 0 0 | * * 12 * * * * * * * | 0 0 2 2 0 0 0 0 0 0 0 0 0 | 0 0 1 2 1 0 0 0 0 0 .x..3.o.. .... | 0 3 0 0 | 0 0 3 0 0 0 0 | * * * 4 * * * * * * | 1 0 0 0 1 1 1 0 0 0 0 0 0 | 1 0 1 0 0 1 1 0 0 0 .xo. .... ....&#x | 0 2 1 0 | 0 0 1 2 0 0 0 | * * * * 6 * * * * * | 0 0 0 0 0 2 0 0 0 2 0 0 0 | 0 0 0 0 0 1 2 1 0 0 .x.o .... ....&#x | 0 2 0 1 | 0 0 1 0 2 0 0 | * * * * * 12 * * * * | 0 0 1 0 0 0 1 1 0 1 0 0 0 | 0 0 1 1 0 0 1 1 0 0 .... .... .o.x&#x | 0 1 0 2 | 0 0 0 0 2 0 1 | * * * * * * 12 * * * | 0 0 0 1 0 0 0 1 1 0 1 0 0 | 0 0 0 1 1 0 0 1 1 0 .ooo3.ooo3.ooo&#x | 0 1 1 1 | 0 0 0 1 1 1 0 | * * * * * * * 12 * * | 0 0 0 0 0 0 0 0 0 2 2 0 0 | 0 0 0 0 0 0 1 2 1 0 .... .... ..ox&#x | 0 0 1 2 | 0 0 0 0 0 2 1 | * * * * * * * * 6 * | 0 0 0 0 0 0 0 0 0 0 2 2 0 | 0 0 0 0 0 0 0 1 2 1 .... ...o3...x | 0 0 0 3 | 0 0 0 0 0 0 3 | * * * * * * * * * 4 | 0 1 0 0 0 0 0 0 1 0 0 1 1 | 0 1 0 0 1 0 0 0 1 1 ------------------+---------+----------------+-------------------------+-------------------------------+-------------------- ox..3oo.. ....&#x ♦ 1 3 0 0 | 3 0 3 0 0 0 0 | 3 0 0 1 0 0 0 0 0 0 | 4 * * * * * * * * * * * * | 1 0 1 0 0 0 0 0 0 0 .... o..o3o..x&#x ♦ 1 0 0 3 | 0 3 0 0 0 0 3 | 0 3 0 0 0 0 0 0 0 1 | * 4 * * * * * * * * * * * | 0 1 0 0 1 0 0 0 0 0 ox.o .... ....&#x ♦ 1 2 0 1 | 2 1 1 0 2 0 0 | 1 0 2 0 0 1 0 0 0 0 | * * 12 * * * * * * * * * * | 0 0 1 1 0 0 0 0 0 0 .... .... oo.x&#x ♦ 1 1 0 2 | 1 2 0 0 2 0 1 | 0 1 2 0 0 0 1 0 0 0 | * * * 12 * * * * * * * * * | 0 0 0 1 1 0 0 0 0 0 .x..3.o..3.o.. ♦ 0 4 0 0 | 0 0 6 0 0 0 0 | 0 0 0 4 0 0 0 0 0 0 | * * * * 1 * * * * * * * * | 1 0 0 0 0 1 0 0 0 0 .xo.3.oo. ....&#x ♦ 0 3 1 0 | 0 0 3 3 0 0 0 | 0 0 0 1 3 0 0 0 0 0 | * * * * * 4 * * * * * * * | 0 0 0 0 0 1 1 0 0 0 .x.o3.o.o ....&#x ♦ 0 3 0 1 | 0 0 3 0 3 0 0 | 0 0 0 1 0 3 0 0 0 0 | * * * * * * 4 * * * * * * | 0 0 1 0 0 0 1 0 0 0 .x.o .... .o.x&#x ♦ 0 2 0 2 | 0 0 1 0 4 0 1 | 0 0 0 0 0 2 2 0 0 0 | * * * * * * * 6 * * * * * | 0 0 0 1 0 0 0 1 0 0 .... .o.o3.o.x&#x ♦ 0 1 0 3 | 0 0 0 0 3 0 3 | 0 0 0 0 0 0 3 0 0 1 | * * * * * * * * 4 * * * * | 0 0 0 0 1 0 0 0 1 0 .xoo .... ....&#x ♦ 0 2 1 1 | 0 0 1 2 2 1 0 | 0 0 0 0 1 1 0 2 0 0 | * * * * * * * * * 12 * * * | 0 0 0 0 0 0 1 1 0 0 .... .... .oox&#x ♦ 0 1 1 2 | 0 0 0 1 2 2 1 | 0 0 0 0 0 0 1 2 1 0 | * * * * * * * * * * 12 * * | 0 0 0 0 0 0 0 1 1 0 .... ..oo3..ox&#x ♦ 0 0 1 3 | 0 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 3 1 | * * * * * * * * * * * 4 * | 0 0 0 0 0 0 0 0 1 1 ...o3...o3...x ♦ 0 0 0 4 | 0 0 0 0 0 0 6 | 0 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * * 1 | 0 1 0 0 0 0 0 0 0 1 ------------------+---------+----------------+-------------------------+-------------------------------+-------------------- ox..3oo..3oo..&#x ♦ 1 4 0 0 | 4 0 6 0 0 0 0 | 6 0 0 4 0 0 0 0 0 0 | 4 0 0 0 1 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * o..o3o..o3o..x&#x ♦ 1 0 0 4 | 0 4 0 0 0 0 6 | 0 6 0 0 0 0 0 0 0 4 | 0 4 0 0 0 0 0 0 0 0 0 0 1 | * 1 * * * * * * * * ox.o3oo.o ....&#x ♦ 1 3 0 1 | 3 1 3 0 3 0 0 | 3 0 3 1 0 3 0 0 0 0 | 1 0 3 0 0 0 1 0 0 0 0 0 0 | * * 4 * * * * * * * ox.o .... oo.x&#x ♦ 1 2 0 2 | 2 2 1 0 4 0 1 | 1 1 4 0 0 2 2 0 0 0 | 0 0 2 2 0 0 0 1 0 0 0 0 0 | * * * 6 * * * * * * .... oo.o3oo.x&#x ♦ 1 1 0 3 | 1 3 0 0 3 0 3 | 0 3 3 0 0 0 3 0 0 1 | 0 1 0 3 0 0 0 0 1 0 0 0 0 | * * * * 4 * * * * * .xo.3.oo.3.oo.&#x ♦ 0 4 1 0 | 0 0 6 4 0 0 0 | 0 0 0 4 6 0 0 0 0 0 | 0 0 0 0 1 4 0 0 0 0 0 0 0 | * * * * * 1 * * * * .xoo3.ooo ....&#x ♦ 0 3 1 1 | 0 0 3 3 3 1 0 | 0 0 0 1 3 3 0 3 0 0 | 0 0 0 0 0 1 1 0 0 3 0 0 0 | * * * * * * 4 * * * .xoo .... .oox&#x ♦ 0 2 1 2 | 0 0 1 2 4 2 1 | 0 0 0 0 1 2 2 4 1 0 | 0 0 0 0 0 0 0 1 0 2 2 0 0 | * * * * * * * 6 * * .... .ooo3.oox&#x ♦ 0 1 1 3 | 0 0 0 1 3 3 3 | 0 0 0 0 0 0 3 3 3 1 | 0 0 0 0 0 0 0 0 1 0 3 1 0 | * * * * * * * * 4 * ..oo3..oo3..ox&#x ♦ 0 0 1 4 | 0 0 0 0 0 4 6 | 0 0 0 0 0 0 0 0 6 4 | 0 0 0 0 0 0 0 0 0 0 0 4 1 | * * * * * * * * * 1
or o...3o...3o... & | 2 * ♦ 8 0 0 | 12 12 0 0 | 8 0 24 0 0 | 2 8 6 .o..3.o..3.o.. & | * 8 ♦ 2 3 3 | 6 6 3 9 | 6 1 18 4 3 | 2 8 6 --------------------+-----+----------+------------+-------------+-------- oo..3oo..3oo..&#x & | 1 1 | 16 * * ♦ 3 3 0 0 | 3 0 9 0 0 | 1 4 3 .x.. .... .... & | 0 2 | * 12 * ♦ 2 0 2 2 | 4 1 4 2 1 | 2 4 2 .o.o3.o.o3.o.o&#x | 0 2 | * * 12 ♦ 0 2 0 4 | 0 0 8 2 2 | 0 4 4 --------------------+-----+----------+------------+-------------+-------- ox.. .... ....&#x & | 1 2 | 2 1 0 | 24 * * * | 2 0 2 0 0 | 1 2 1 oo.o3oo.o3oo.o&#x & | 1 2 | 2 0 1 | * 24 * * | 0 0 4 0 0 | 0 2 2 .x..3.o.. .... & | 0 3 | 0 3 0 | * * 8 * | 2 1 0 1 0 | 2 2 0 .x.o .... ....&#x & | 0 3 | 0 1 2 | * * * 24 | 0 0 2 1 1 | 0 2 2 --------------------+-----+----------+------------+-------------+-------- ox..3oo.. ....&#x & ♦ 1 3 | 3 3 0 | 3 0 1 0 | 16 * * * * | 1 1 0 .x..3.o..3.o.. & ♦ 0 4 | 0 6 0 | 0 0 4 0 | * 2 * * * | 2 0 0 ox.o .... ....&#x & ♦ 1 3 | 3 1 2 | 1 2 0 1 | * * 48 * * | 0 1 1 .x.o3.o.o ....&#x & ♦ 0 4 | 0 3 3 | 0 0 1 3 | * * * 8 * | 0 2 0 .x.o .... .o.x&#x ♦ 0 4 | 0 2 4 | 0 0 0 4 | * * * * 6 | 0 0 2 --------------------+-----+----------+------------+-------------+-------- ox..3oo..3oo..&#x & ♦ 1 4 | 4 6 0 | 6 0 4 0 | 4 1 0 0 0 | 4 * * ox.o3oo.o ....&#x & ♦ 1 4 | 4 3 3 | 3 3 1 3 | 1 0 3 1 0 | * 16 * ox.o .... oo.x&#x & ♦ 1 4 | 4 2 4 | 2 4 0 4 | 0 0 4 0 1 | * * 12
o(xo)o3o(oo)o3o(ox)o&#xt → both heights = 1/sqrt(2) = 0.707107 (pt || (tet || dual tet) || pt) o(..).3o(..).3o(..). & | 2 * ♦ 4 4 0 0 | 6 6 12 0 0 | 4 4 12 12 0 0 0 | 1 1 4 6 4 .(o.).3.(o.).3.(o.). & | * 8 ♦ 1 1 3 3 | 3 3 6 3 9 | 3 3 9 9 1 4 3 | 1 1 4 6 4 ---------------------------+-----+-----------+---------------+-----------------+----------- o(o.).3o(o.).3o(o.).&#x & | 1 1 | 8 * * * ♦ 3 0 3 0 0 | 3 0 6 3 0 0 0 | 1 0 3 3 1 o(.o).3o(.o).3o(.o).&#x & | 1 1 | * 8 * * ♦ 0 3 3 0 0 | 0 3 3 6 0 0 0 | 0 1 1 3 3 .(x.). .(..). .(..). & | 0 2 | * * 12 * ♦ 1 1 0 2 2 | 2 2 2 2 1 2 1 | 1 1 2 2 2 .(oo).3.(oo).3.(oo).&#x | 0 2 | * * * 12 ♦ 0 0 2 0 4 | 0 0 4 4 0 2 2 | 0 0 2 4 2 ---------------------------+-----+-----------+---------------+-----------------+----------- o(x.). .(..). .(..).&#x & | 1 2 | 2 0 1 0 | 12 * * * * | 2 0 2 0 0 0 0 | 1 0 2 1 0 .(..). .(..). o(.x).&#x & | 1 2 | 0 2 1 0 | * 12 * * * | 0 2 0 2 0 0 0 | 0 1 0 1 2 o(oo).3o(oo).3o(oo).&#x & | 1 2 | 1 1 0 1 | * * 24 * * | 0 0 2 2 0 0 0 | 0 0 1 2 1 .(x.).3.(o.). .(..). & | 0 3 | 0 0 3 0 | * * * 8 * | 1 1 0 0 1 1 0 | 1 1 1 0 1 .(xo). .(..). .(..).&#x & | 0 3 | 0 0 1 2 | * * * * 24 | 0 0 1 1 0 1 1 | 0 0 1 2 1 ---------------------------+-----+-----------+---------------+-----------------+----------- o(x.).3o(o.). .(..).&#x & ♦ 1 3 | 3 0 3 0 | 3 0 0 1 0 | 8 * * * * * * | 1 0 1 0 0 .(..). o(.o).3o(.x).&#x & ♦ 1 3 | 0 3 3 0 | 0 3 0 1 0 | * 8 * * * * * | 0 1 0 0 1 o(xo). .(..). .(..).&#x & ♦ 1 3 | 2 1 1 2 | 1 0 2 0 1 | * * 24 * * * * | 0 0 1 1 0 .(..). .(..). o(ox).&#x & ♦ 1 3 | 1 2 1 2 | 0 1 2 0 1 | * * * 24 * * * | 0 0 0 1 1 .(x.).3.(o.).3.(o.). & ♦ 0 4 | 0 0 6 0 | 0 0 0 4 0 | * * * * 2 * * | 1 1 0 0 0 .(xo).3.(oo). .(..).&#x & ♦ 0 4 | 0 0 3 3 | 0 0 0 1 3 | * * * * * 8 * | 0 0 1 0 1 .(xo). .(..). .(ox).&#x ♦ 0 4 | 0 0 2 4 | 0 0 0 0 4 | * * * * * * 6 | 0 0 0 2 0 ---------------------------+-----+-----------+---------------+-----------------+----------- o(x.).3o(o.).3o(o.).&#x & ♦ 1 4 | 4 0 6 0 | 6 0 0 4 0 | 4 0 0 0 1 0 0 | 2 * * * * o(.o).3o(.o).3o(.x).&#x & ♦ 1 4 | 0 4 6 0 | 0 6 0 4 0 | 0 4 0 0 1 0 0 | * 2 * * * o(xo).3o(oo). .(..).&#x & ♦ 1 4 | 3 1 3 3 | 3 0 3 1 3 | 1 0 3 0 0 1 0 | * * 8 * * o(xo). .(..). o(ox).&#x & ♦ 1 4 | 2 2 2 4 | 1 1 4 0 4 | 0 0 2 2 0 0 1 | * * * 12 * .(..). o(oo).3o(ox).&#x & ♦ 1 4 | 1 3 3 3 | 0 3 3 1 3 | 0 1 0 3 0 1 0 | * * * * 8
xoxo oxoo3ooox&#xr → all cyclical heights = sqrt(5/12) = 0.645497 in fact a rhomb with diagonals height(1,3) = 1 height(2,4) = sqrt(2/3) = 0.816497 o... o...3o... | 2 * * * ♦ 1 3 1 3 0 0 0 0 0 0 | 3 3 3 3 3 6 3 0 0 0 0 0 0 0 0 0 | 3 1 3 1 3 6 3 3 3 6 0 0 0 0 0 0 0 | 1 1 1 3 3 1 3 3 0 0 0 0 .o.. .o..3.o.. | * 3 * * ♦ 0 2 0 0 2 2 2 0 0 0 | 1 4 0 0 2 4 0 1 1 4 2 1 4 0 0 0 | 2 2 0 0 4 2 4 2 0 4 2 2 2 4 2 0 0 | 1 0 2 2 1 0 4 2 1 2 1 0 ..o. ..o.3..o. | * * 2 * ♦ 0 0 1 0 0 3 0 1 3 0 | 0 0 0 0 3 0 3 0 3 3 0 0 6 3 3 0 | 0 0 0 0 3 0 0 0 3 6 3 1 6 3 3 3 1 | 0 0 1 0 0 1 3 3 1 3 3 1 ...o ...o3...o | * * * 3 ♦ 0 0 0 2 0 0 2 0 2 2 | 0 0 1 4 0 4 2 0 0 0 1 2 4 1 4 1 | 0 0 2 2 0 2 2 4 4 4 0 0 2 2 4 2 2 | 0 1 0 1 2 2 2 4 0 1 2 1 ------------------+---------+---------------------+-----------------------------------+------------------------------------+------------------------ x... .... .... | 2 0 0 0 | 1 * * * * * * * * * ♦ 3 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3 0 3 0 0 6 0 0 0 0 0 0 0 0 0 0 0 | 1 1 0 3 3 0 0 0 0 0 0 0 oo.. oo..3oo..&#x | 1 1 0 0 | * 6 * * * * * * * * ♦ 1 2 0 0 1 2 0 0 0 0 0 0 0 0 0 0 | 2 1 0 0 2 2 2 1 0 2 0 0 0 0 0 0 0 | 1 0 1 2 1 0 2 1 0 0 0 0 o.o. o.o.3o.o.&#x | 1 0 1 0 | * * 2 * * * * * * * ♦ 0 0 0 0 3 0 3 0 0 0 0 0 0 0 0 0 | 0 0 0 0 3 0 0 0 3 6 0 0 0 0 0 0 0 | 0 0 1 0 0 1 3 3 0 0 0 0 o..o o..o3o..o&#x | 1 0 0 1 | * * * 6 * * * * * * ♦ 0 0 1 2 0 2 1 0 0 0 0 0 0 0 0 0 | 0 0 2 1 0 2 1 2 2 2 0 0 0 0 0 0 0 | 0 1 0 1 2 1 1 2 0 0 0 0 .... .x.. .... | 0 2 0 0 | * * * * 3 * * * * * ♦ 0 2 0 0 0 0 0 1 0 2 1 0 0 0 0 0 | 1 2 0 0 2 0 2 0 0 0 1 2 0 2 0 0 0 | 1 0 2 1 0 0 2 0 1 1 0 0 .oo. .oo.3.oo.&#x | 0 1 1 0 | * * * * * 6 * * * * ♦ 0 0 0 0 1 0 0 0 1 2 0 0 2 0 0 0 | 0 0 0 0 2 0 0 0 0 2 2 1 2 2 1 0 0 | 0 0 1 0 0 0 2 1 1 2 1 0 .o.o .o.o3.o.o&#x | 0 1 0 1 | * * * * * * 6 * * * ♦ 0 0 0 0 0 2 0 0 0 0 1 1 2 0 0 0 | 0 0 0 0 0 1 2 2 0 2 0 0 1 2 2 0 0 | 0 0 0 1 1 0 2 2 0 1 1 0 ..x. .... .... | 0 0 2 0 | * * * * * * * 1 * * ♦ 0 0 0 0 0 0 0 0 3 0 0 0 0 3 0 0 | 0 0 0 0 0 0 0 0 0 0 3 0 6 0 0 3 0 | 0 0 0 0 0 0 0 0 1 3 3 1 ..oo ..oo3..oo&#x | 0 0 1 1 | * * * * * * * * 6 * ♦ 0 0 0 0 0 0 1 0 0 0 0 0 2 1 2 0 | 0 0 0 0 0 0 0 0 2 2 0 0 2 1 2 2 1 | 0 0 0 0 0 1 1 2 0 1 2 1 .... .... ...x | 0 0 0 2 | * * * * * * * * * 3 ♦ 0 0 0 2 0 0 0 0 0 0 0 1 0 0 2 1 | 0 0 1 2 0 0 0 2 2 0 0 0 0 0 2 1 2 | 0 1 0 0 1 2 0 2 0 0 1 1 ------------------+---------+---------------------+-----------------------------------+------------------------------------+------------------------ xo.. .... ....&#x | 2 1 0 0 | 1 2 0 0 0 0 0 0 0 0 | 3 * * * * * * * * * * * * * * * | 2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 | 1 0 0 2 1 0 0 0 0 0 0 0 .... ox.. ....&#x | 1 2 0 0 | 0 2 0 0 1 0 0 0 0 0 | * 6 * * * * * * * * * * * * * * | 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0 1 0 0 0 0 0 x..o .... ....&#x | 2 0 0 1 | 1 0 0 2 0 0 0 0 0 0 | * * 3 * * * * * * * * * * * * * | 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 1 2 0 0 0 0 0 0 0 .... .... o..x&#x | 1 0 0 2 | 0 0 0 2 0 0 0 0 0 1 | * * * 6 * * * * * * * * * * * * | 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 | 0 1 0 0 1 1 0 1 0 0 0 0 ooo. ooo.3ooo.&#x | 1 1 1 0 | 0 1 1 0 0 1 0 0 0 0 | * * * * 6 * * * * * * * * * * * | 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 | 0 0 1 0 0 0 2 1 0 0 0 0 oo.o oo.o3oo.o&#x | 1 1 0 1 | 0 1 0 1 0 0 1 0 0 0 | * * * * * 12 * * * * * * * * * * | 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 | 0 0 0 1 1 0 1 1 0 0 0 0 o.oo o.oo3o.oo&#x | 1 0 1 1 | 0 0 1 1 0 0 0 0 1 0 | * * * * * * 6 * * * * * * * * * | 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 | 0 0 0 0 0 1 1 2 0 0 0 0 .... .x..3.o.. | 0 3 0 0 | 0 0 0 0 3 0 0 0 0 0 | * * * * * * * 1 * * * * * * * * | 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 | 1 0 2 0 0 0 0 0 1 0 0 0 .ox. .... ....&#x | 0 1 2 0 | 0 0 0 0 0 2 0 1 0 0 | * * * * * * * * 3 * * * * * * * | 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 | 0 0 0 0 0 0 0 0 1 2 1 0 .... .xo. ....&#x | 0 2 1 0 | 0 0 0 0 1 2 0 0 0 0 | * * * * * * * * * 6 * * * * * * | 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 | 0 0 1 0 0 0 1 0 1 1 0 0 .... .x.o ....&#x | 0 2 0 1 | 0 0 0 0 1 0 2 0 0 0 | * * * * * * * * * * 3 * * * * * | 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 | 0 0 0 1 0 0 2 0 0 1 0 0 .... .... .o.x&#x | 0 1 0 2 | 0 0 0 0 0 0 2 0 0 1 | * * * * * * * * * * * 3 * * * * | 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 | 0 0 0 0 1 0 0 2 0 0 1 0 .ooo .ooo3.ooo&#x | 0 1 1 1 | 0 0 0 0 0 1 1 0 1 0 | * * * * * * * * * * * * 12 * * * | 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 | 0 0 0 0 0 0 1 1 0 1 1 0 ..xo .... ....&#x | 0 0 2 1 | 0 0 0 0 0 0 0 1 2 0 | * * * * * * * * * * * * * 3 * * | 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 | 0 0 0 0 0 0 0 0 0 1 2 1 .... .... ..ox&#x | 0 0 1 2 | 0 0 0 0 0 0 0 0 2 1 | * * * * * * * * * * * * * * 6 * | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 | 0 0 0 0 0 1 0 1 0 0 1 1 .... ...o3...x | 0 0 0 3 | 0 0 0 0 0 0 0 0 0 3 | * * * * * * * * * * * * * * * 1 | 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 | 0 1 0 0 0 2 0 0 0 0 0 1 ------------------+---------+---------------------+-----------------------------------+------------------------------------+------------------------ xo.. ox.. ....&#x ♦ 2 2 0 0 | 1 4 0 0 1 0 0 0 0 0 | 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3 * * * * * * * * * * * * * * * * | 1 0 0 1 0 0 0 0 0 0 0 0 .... ox..3oo..&#x ♦ 1 3 0 0 | 0 3 0 0 3 0 0 0 0 0 | 0 3 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | * 2 * * * * * * * * * * * * * * * | 1 0 1 0 0 0 0 0 0 0 0 0 x..o .... o..x&#x ♦ 2 0 0 2 | 1 0 0 4 0 0 0 0 0 1 | 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 | * * 3 * * * * * * * * * * * * * * | 0 1 0 0 1 0 0 0 0 0 0 0 .... o..o3o..x&#x ♦ 1 0 0 3 | 0 0 0 3 0 0 0 0 0 3 | 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 1 | * * * 2 * * * * * * * * * * * * * | 0 1 0 0 0 1 0 0 0 0 0 0 .... oxo. ....&#x ♦ 1 2 1 0 | 0 2 1 0 1 2 0 0 0 0 | 0 1 0 0 2 0 0 0 0 1 0 0 0 0 0 0 | * * * * 6 * * * * * * * * * * * * | 0 0 1 0 0 0 1 0 0 0 0 0 xo.o .... ....&#x ♦ 2 1 0 1 | 1 2 0 2 0 0 1 0 0 0 | 1 0 1 0 0 2 0 0 0 0 0 0 0 0 0 0 | * * * * * 6 * * * * * * * * * * * | 0 0 0 1 1 0 0 0 0 0 0 0 .... ox.o ....&#x ♦ 1 2 0 1 | 0 2 0 1 1 0 2 0 0 0 | 0 1 0 0 0 2 0 0 0 0 1 0 0 0 0 0 | * * * * * * 6 * * * * * * * * * * | 0 0 0 1 0 0 1 0 0 0 0 0 .... .... oo.x&#x ♦ 1 1 0 2 | 0 1 0 2 0 0 2 0 0 1 | 0 0 0 1 0 2 0 0 0 0 0 1 0 0 0 0 | * * * * * * * 6 * * * * * * * * * | 0 0 0 0 1 0 0 1 0 0 0 0 .... .... o.ox&#x ♦ 1 0 1 2 | 0 0 1 2 0 0 0 0 2 1 | 0 0 0 1 0 0 2 0 0 0 0 0 0 0 1 0 | * * * * * * * * 6 * * * * * * * * | 0 0 0 0 0 1 0 1 0 0 0 0 oooo oooo3oooo&#x ♦ 1 1 1 1 | 0 1 1 1 0 1 1 0 1 0 | 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 | * * * * * * * * * 12 * * * * * * * | 0 0 0 0 0 0 1 1 0 0 0 0 .ox. .xo. ....&#x ♦ 0 2 2 0 | 0 0 0 0 1 4 0 1 0 0 | 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 | * * * * * * * * * * 3 * * * * * * | 0 0 0 0 0 0 0 0 1 1 0 0 .... .xo.3.oo.&#x ♦ 0 3 1 0 | 0 0 0 0 3 3 0 0 0 0 | 0 0 0 0 0 0 0 1 0 3 0 0 0 0 0 0 | * * * * * * * * * * * 2 * * * * * | 0 0 1 0 0 0 0 0 1 0 0 0 .oxo .... ....&#x ♦ 0 1 2 1 | 0 0 0 0 0 2 1 1 2 0 | 0 0 0 0 0 0 0 0 1 0 0 0 2 1 0 0 | * * * * * * * * * * * * 6 * * * * | 0 0 0 0 0 0 0 0 0 1 1 0 .... .xoo ....&#x ♦ 0 2 1 1 | 0 0 0 0 1 2 2 0 1 0 | 0 0 0 0 0 0 0 0 0 1 1 0 2 0 0 0 | * * * * * * * * * * * * * 6 * * * | 0 0 0 0 0 0 1 0 0 1 0 0 .... .... .oox&#x ♦ 0 1 1 2 | 0 0 0 0 0 1 2 0 2 1 | 0 0 0 0 0 0 0 0 0 0 0 1 2 0 1 0 | * * * * * * * * * * * * * * 6 * * | 0 0 0 0 0 0 0 1 0 0 1 0 ..xo .... ..ox&#x ♦ 0 0 2 2 | 0 0 0 0 0 0 0 1 4 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 | * * * * * * * * * * * * * * * 3 * | 0 0 0 0 0 0 0 0 0 0 1 1 .... ..oo3..ox&#x ♦ 0 0 1 3 | 0 0 0 0 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 | * * * * * * * * * * * * * * * * 2 | 0 0 0 0 0 1 0 0 0 0 0 1 ------------------+---------+---------------------+-----------------------------------+------------------------------------+------------------------ xo.. ox..3oo..&#x ♦ 2 3 0 0 | 1 6 0 0 3 0 0 0 0 0 | 3 6 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * x..o o..o3o..x&#x ♦ 2 0 0 3 | 1 0 0 6 0 0 0 0 0 3 | 0 0 3 6 0 0 0 0 0 0 0 0 0 0 0 1 | 0 0 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 1 * * * * * * * * * * .... oxo.3ooo.&#x ♦ 1 3 1 0 | 0 3 1 0 3 3 0 0 0 0 | 0 3 0 0 3 0 0 1 0 3 0 0 0 0 0 0 | 0 1 0 0 3 0 0 0 0 0 0 1 0 0 0 0 0 | * * 2 * * * * * * * * * xo.o ox.o ....&#x ♦ 2 2 0 1 | 1 4 0 2 1 0 2 0 0 0 | 2 2 1 0 0 4 0 0 0 0 1 0 0 0 0 0 | 1 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 | * * * 3 * * * * * * * * xo.o .... oo.x&#x ♦ 2 1 0 2 | 1 2 0 4 0 0 2 0 0 1 | 1 0 2 2 0 4 0 0 0 0 0 1 0 0 0 0 | 0 0 1 0 0 2 0 2 0 0 0 0 0 0 0 0 0 | * * * * 3 * * * * * * * .... o.oo3o.ox&#x ♦ 1 0 1 3 | 0 0 1 3 0 0 0 0 3 3 | 0 0 0 3 0 0 3 0 0 0 0 0 0 0 3 1 | 0 0 0 1 0 0 0 0 3 0 0 0 0 0 0 0 1 | * * * * * 2 * * * * * * .... oxoo ....&#x ♦ 1 2 1 1 | 0 2 1 1 1 2 2 0 1 0 | 0 1 0 0 2 2 1 0 0 1 1 0 2 0 0 0 | 0 0 0 0 1 0 1 0 0 2 0 0 0 1 0 0 0 | * * * * * * 6 * * * * * .... .... ooox&#x ♦ 1 1 1 2 | 0 1 1 2 0 1 2 0 2 1 | 0 0 0 1 1 2 2 0 0 0 0 1 2 0 1 0 | 0 0 0 0 0 0 0 1 1 2 0 0 0 0 1 0 0 | * * * * * * * 6 * * * * .ox. .xo.3.oo.&#x ♦ 0 3 2 0 | 0 0 0 0 3 6 0 1 0 0 | 0 0 0 0 0 0 0 1 3 6 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 3 2 0 0 0 0 0 | * * * * * * * * 1 * * * .oxo .xoo ....&#x ♦ 0 2 2 1 | 0 0 0 0 1 4 2 1 2 0 | 0 0 0 0 0 0 0 0 2 2 1 0 4 1 0 0 | 0 0 0 0 0 0 0 0 0 0 1 0 2 2 0 0 0 | * * * * * * * * * 3 * * .oxo .... .oox&#x ♦ 0 1 2 2 | 0 0 0 0 0 2 2 1 4 1 | 0 0 0 0 0 0 0 0 1 0 0 1 4 2 2 0 | 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 1 0 | * * * * * * * * * * 3 * ..xo ..oo3..ox&#x ♦ 0 0 2 3 | 0 0 0 0 0 0 0 1 6 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 3 6 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 | * * * * * * * * * * * 1
xo4oo ox3oo4oo&#zx → height = 0 (tegum sum of {4} and perp oct) (tegum product of {4} with oct) o.4o. o.3o.4o. | 4 * ♦ 2 6 0 | 12 12 0 | 24 8 | 16 .o4.o .o3.o4.o | * 6 ♦ 0 4 4 | 4 16 4 | 16 16 | 16 ------------------+-----+---------+---------+-------+--- x. .. .. .. .. | 2 0 | 4 * * ♦ 6 0 0 | 12 0 | 8 oo4oo oo3oo4oo&#x | 1 1 | * 24 * ♦ 2 4 0 | 8 4 | 8 .. .. .x .. .. | 0 2 | * * 12 ♦ 0 4 2 | 4 8 | 8 ------------------+-----+---------+---------+-------+--- xo .. .. .. ..&#x | 2 1 | 1 2 0 | 24 * * | 4 0 | 4 .. .. ox .. ..&#x | 1 2 | 0 2 1 | * 48 * | 2 2 | 4 .. .. .x3.o .. | 0 3 | 0 0 3 | * * 8 | 0 4 | 4 ------------------+-----+---------+---------+-------+--- xo .. ox .. ..&#x ♦ 2 2 | 1 4 1 | 2 2 0 | 48 * | 2 .. .. ox3oo ..&#x ♦ 1 3 | 0 3 3 | 0 3 1 | * 32 | 2 ------------------+-----+---------+---------+-------+--- xo .. ox3oo ..&#x ♦ 2 3 | 1 6 3 | 3 6 1 | 3 2 | 32
xo xo oo3ox3oo&#zx → height = 0 (tegum sum of {4} and perp oct) (tegum product of {4} with oct) o. o. o.3o.3o. | 4 * ♦ 1 1 6 0 | 6 6 12 0 0 | 12 12 4 4 | 4 4 4 4 .o .o .o3.o3.o | * 6 ♦ 0 0 4 4 | 2 2 16 2 2 | 8 8 8 8 | 4 4 4 4 ------------------+-----+-----------+--------------+-------------+-------- x. .. .. .. .. | 2 0 | 2 * * * ♦ 6 0 0 0 0 | 12 0 0 0 | 4 4 0 0 .. x. .. .. .. | 2 0 | * 2 * * ♦ 0 6 0 0 0 | 0 12 0 0 | 0 0 4 4 oo oo oo3oo3oo&#x | 1 1 | * * 24 * ♦ 1 1 4 0 0 | 4 4 2 2 | 2 2 2 2 .. .. .. .x .. | 0 2 | * * * 12 ♦ 0 0 4 1 1 | 2 2 4 4 | 2 2 2 2 ------------------+-----+-----------+--------------+-------------+-------- xo .. .. .. ..&#x | 2 1 | 1 0 2 0 | 12 * * * * | 4 0 0 0 | 2 2 0 0 .. xo .. .. ..&#x | 2 1 | 0 1 2 0 | * 12 * * * | 0 4 0 0 | 0 0 2 2 .. .. .. ox ..&#x | 1 2 | 0 0 2 1 | * * 48 * * | 1 1 1 1 | 1 1 1 1 .. .. .o3.x .. | 0 3 | 0 0 0 3 | * * * 4 * | 0 0 4 0 | 2 0 2 0 .. .. .. .x3.o | 0 3 | 0 0 0 3 | * * * * 4 | 0 0 0 4 | 0 2 0 2 ------------------+-----+-----------+--------------+-------------+-------- xo .. .. ox ..&#x ♦ 2 2 | 1 0 4 1 | 2 0 2 0 0 | 24 * * * | 1 1 0 0 .. xo .. ox ..&#x ♦ 2 2 | 0 1 4 1 | 0 2 2 0 0 | * 24 * * | 0 0 1 1 .. .. oo3ox ..&#x ♦ 1 3 | 0 0 3 3 | 0 0 3 1 0 | * * 16 * | 1 0 1 0 .. .. .. ox3oo&#x ♦ 1 3 | 0 0 3 3 | 0 0 3 0 1 | * * * 16 | 0 1 0 1 ------------------+-----+-----------+--------------+-------------+-------- xo .. oo3ox ..&#x ♦ 2 3 | 1 0 6 3 | 3 0 6 1 0 | 3 0 2 0 | 8 * * * xo .. .. ox3oo&#x ♦ 2 3 | 1 0 6 3 | 3 0 6 0 1 | 3 0 0 2 | * 8 * * .. xo oo3ox ..&#x ♦ 2 3 | 0 1 6 3 | 0 3 6 1 0 | 0 3 2 0 | * * 8 * .. xo .. ox3oo&#x ♦ 2 3 | 0 1 6 3 | 0 3 6 0 1 | 0 3 0 2 | * * * 8
o(xo)o4o(oo)o o(ox)o4o(oo)o&#xt → both heights = 1/sqrt(2) = 0.707107 (pt || (tegum product of two {4}) || pt) o(..).4o(..). o(..).4o(..). | 1 * * * ♦ 4 4 0 0 0 0 0 | 4 16 4 0 0 0 0 0 | 16 16 0 0 0 | 16 0 .(o.).4.(o.). .(o.).4.(o.). | * 4 * * ♦ 1 0 2 4 1 0 0 | 2 4 0 8 4 2 4 0 | 8 4 8 8 4 | 8 8 .(.o).4.(.o). .(.o).4.(.o). | * * 4 * ♦ 0 1 0 4 0 2 1 | 0 4 2 4 8 0 4 2 | 4 8 8 4 8 | 8 8 .(..)o4.(..)o .(..)o4.(..)o | * * * 1 ♦ 0 0 0 0 4 0 4 | 0 0 0 0 0 4 16 4 | 0 0 0 16 16 | 0 16 -------------------------------+---------+----------------+---------------------+----------------+------ o(o.).4o(o.). o(o.).4o(o.).&#x | 1 1 0 0 | 4 * * * * * * ♦ 2 4 0 0 0 0 0 0 | 8 4 0 0 0 | 8 0 o(.o).4o(.o). o(.o).4o(.o).&#x | 1 0 1 0 | * 4 * * * * * ♦ 0 4 2 0 0 0 0 0 | 4 8 0 0 0 | 4 0 .(x.). .(..). .(..). .(..). | 0 2 0 0 | * * 4 * * * * ♦ 1 0 0 4 0 1 0 0 | 4 0 4 4 0 | 4 4 .(oo).4.(oo). .(oo).4.(oo).&#x | 0 1 1 0 | * * * 16 * * * ♦ 0 1 0 2 2 0 1 0 | 2 2 4 2 2 | 4 4 .(o.)o4.(o.)o .(o.)o4.(o.)o&#x | 0 1 0 1 | * * * * 4 * * ♦ 0 0 0 0 0 2 4 0 | 0 0 0 8 4 | 0 8 .(..). .(..). .(.x). .(..). | 0 0 2 0 | * * * * * 4 * ♦ 0 0 1 0 4 0 0 1 | 0 4 4 0 4 | 4 4 .(.o)o4.(.o)o .(.o)o4.(.o)o&#x | 0 0 1 1 | * * * * * * 4 ♦ 0 0 0 0 0 0 4 2 | 0 0 0 4 8 | 0 8 -------------------------------+---------+----------------+---------------------+----------------+------ o(x.). .(..). .(..). .(..).&#x | 1 2 0 0 | 2 0 1 0 0 0 0 | 4 * * * * * * * | 4 0 0 0 0 | 4 0 o(oo).4o(oo). o(oo).4o(oo).&#x | 1 1 1 0 | 1 1 0 1 0 0 0 | * 16 * * * * * * | 2 2 0 0 0 | 4 0 .(..). .(..). o(.x). .(..).&#x | 1 0 2 0 | 0 2 0 0 0 1 0 | * * 4 * * * * * | 0 4 0 0 0 | 4 0 .(xo). .(..). .(..). .(..).&#x | 0 2 1 0 | 0 0 1 2 0 0 0 | * * * 16 * * * * | 1 0 2 1 0 | 2 2 .(..). .(..). .(ox). .(..).&#x | 0 1 2 0 | 0 0 0 2 0 1 0 | * * * * 16 * * * | 0 1 2 0 1 | 2 2 .(x.)o .(..). .(..). .(..).&#x | 0 2 0 1 | 0 0 1 0 2 0 0 | * * * * * 4 * * | 0 0 0 4 0 | 0 4 .(oo)o4.(oo)o .(oo)o4.(oo)o&#x | 0 1 1 1 | 0 0 0 1 1 0 1 | * * * * * * 16 * | 0 0 0 2 2 | 0 4 .(..). .(..). .(.x)o .(..).&#x | 0 0 2 1 | 0 0 0 0 0 1 2 | * * * * * * * 4 | 0 0 0 0 4 | 0 4 -------------------------------+---------+----------------+---------------------+----------------+------ o(xo). .(..). .(..). .(..).&#x ♦ 1 2 1 0 | 2 1 1 2 0 0 0 | 1 2 0 1 0 0 0 0 | 16 * * * * | 2 0 .(..). .(..). o(ox). .(..).&#x ♦ 1 1 2 0 | 1 2 0 2 0 1 0 | 0 2 1 0 1 0 0 0 | * 16 * * * | 2 0 .(xo). .(..). .(ox). .(..).&#x ♦ 0 2 2 0 | 0 0 1 4 0 1 0 | 0 0 0 2 2 0 0 0 | * * 16 * * | 1 1 .(xo)o .(..). .(..). .(..).&#x ♦ 0 2 1 1 | 0 0 1 2 2 0 1 | 0 0 0 1 0 1 2 0 | * * * 16 * | 0 2 .(..). .(..). .(ox)o .(..).&#x ♦ 0 1 2 1 | 0 0 0 2 1 1 2 | 0 0 0 0 1 0 2 1 | * * * * 16 | 0 2 -------------------------------+---------+----------------+---------------------+----------------+------ o(xo). .(..). o(ox). .(..).&#x ♦ 1 2 2 0 | 2 2 1 4 0 1 0 | 1 4 1 2 2 0 0 0 | 2 2 1 0 0 | 16 * .(xo)o .(..). .(ox)o .(..).&#x ♦ 0 2 2 1 | 0 0 1 4 2 1 2 | 0 0 0 2 2 1 4 1 | 0 0 1 2 2 | * 16
ooq xoo4ooo oxo4ooo&#zx → heights = 0 (tegum sum of 2 perp {4} and a perp q-line) o.. o..4o.. o..4o.. & | 8 * ♦ 2 4 2 | 12 4 8 | 8 24 | 16 ..o ..o4..o ..o4..o | * 2 ♦ 0 0 8 | 0 8 16 | 0 32 | 16 --------------------------+-----+---------+----------+-------+--- ... x.. ... ... ... & | 2 0 | 8 * * ♦ 4 2 0 | 4 8 | 8 oo. oo.4oo. oo.4oo.&#x | 2 0 | * 16 * ♦ 4 0 2 | 4 8 | 8 o.o o.o4o.o o.o4o.o&#x & | 1 1 | * * 16 ♦ 0 2 4 | 0 12 | 8 --------------------------+-----+---------+----------+-------+--- ... xo. ... ... ...&#x & | 3 0 | 1 2 0 | 32 * * | 2 2 | 4 ... x.o ... ... ...&#x & | 2 1 | 1 0 2 | * 16 * | 0 4 | 4 ooo ooo4ooo ooo4ooo&#x | 2 1 | 0 1 2 | * * 32 | 0 4 | 4 --------------------------+-----+---------+----------+-------+--- ... xo. ... ox. ...&#x ♦ 4 0 | 2 4 0 | 4 0 0 | 16 * | 2 ... xoo ... ... ...&#x & ♦ 3 1 | 1 2 3 | 1 1 2 | * 64 | 2 --------------------------+-----+---------+----------+-------+--- ... xoo ... oxo ...&#x ♦ 4 1 | 2 4 4 | 4 2 4 | 1 4 | 32
o(xo)o o(xo)o o(ox)o o(ox)o&#xt → both heights = 1/sqrt(2) = 0.707107 (pt || (tegum product of two {4}) || pt) o(..). o(..). o(..). o(..). | 1 * * * ♦ 4 4 0 0 0 0 0 0 0 | 2 2 16 2 2 0 0 0 0 0 0 0 0 0 | 8 8 8 8 0 0 0 0 0 0 0 0 | 4 4 4 4 0 0 0 0 .(o.). .(o.). .(o.). .(o.). | * 4 * * ♦ 1 0 1 1 4 1 0 0 0 | 1 1 4 0 0 4 4 2 2 1 1 4 0 0 | 4 4 2 2 2 2 2 2 4 4 2 2 | 2 2 2 2 2 2 2 2 .(.o). .(.o). .(.o). .(.o). | * * 4 * ♦ 0 1 0 0 4 0 1 1 1 | 0 0 4 1 1 2 2 4 4 0 0 4 1 1 | 2 2 4 4 2 2 2 2 2 2 4 4 | 2 2 2 2 2 2 2 2 .(..)o .(..)o .(..)o .(..)o | * * * 1 ♦ 0 0 0 0 0 4 0 0 4 | 0 0 0 0 0 0 0 0 0 2 2 16 2 2 | 0 0 0 0 0 0 0 0 8 8 8 8 | 0 0 0 0 4 4 4 4 -------------------------------+---------+--------------------+-------------------------------+-------------------------+---------------- o(o.). o(o.). o(o.). o(o.).&#x | 1 1 0 0 | 4 * * * * * * * * ♦ 1 1 4 0 0 0 0 0 0 0 0 0 0 0 | 4 4 2 2 0 0 0 0 0 0 0 0 | 2 2 2 2 0 0 0 0 o(.o). o(.o). o(.o). o(.o).&#x | 1 0 1 0 | * 4 * * * * * * * ♦ 0 0 4 1 1 0 0 0 0 0 0 0 0 0 | 2 2 4 4 0 0 0 0 0 0 0 0 | 2 2 2 2 0 0 0 0 .(x.). .(..). .(..). .(..). | 0 2 0 0 | * * 2 * * * * * * ♦ 1 0 0 0 0 4 0 0 0 1 0 0 0 0 | 4 0 0 0 2 2 0 0 4 0 0 0 | 2 2 0 0 2 2 0 0 .(..). .(x.). .(..). .(..). | 0 2 0 0 | * * * 2 * * * * * ♦ 0 1 0 0 0 0 4 0 0 0 1 0 0 0 | 0 4 0 0 0 0 0 2 2 0 4 0 | 0 0 2 2 0 0 2 2 .(oo). .(oo). .(oo). .(oo).&#x | 0 1 1 0 | * * * * 16 * * * * ♦ 0 0 1 0 0 1 1 1 1 0 0 1 0 0 | 1 1 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1 1 1 1 .(o.)o .(o.)o .(o.)o .(o.)o&#x | 0 1 0 1 | * * * * * 4 * * * ♦ 0 0 0 0 0 0 0 0 0 1 1 4 0 0 | 0 0 0 0 0 0 0 0 4 4 2 2 | 0 0 0 0 2 2 2 2 .(..). .(..). .(.x). .(..). | 0 0 2 0 | * * * * * * 2 * * ♦ 0 0 0 1 0 0 0 4 0 0 0 0 1 0 | 0 0 4 0 2 0 2 0 0 0 4 0 | 2 0 2 0 2 0 2 0 .(..). .(..). .(..). .(.x). | 0 0 2 0 | * * * * * * * 2 * ♦ 0 0 0 0 1 0 0 0 4 0 0 0 0 1 | 0 0 0 4 0 2 0 2 0 0 0 4 | 0 2 0 2 0 2 0 2 .(.o)o .(.o)o .(.o)o .(.o)o&#x | 0 0 1 1 | * * * * * * * * 4 ♦ 0 0 0 0 0 0 0 0 0 0 0 4 1 1 | 0 0 0 0 0 0 0 0 2 2 4 4 | 0 0 0 0 2 2 2 2 -------------------------------+---------+--------------------+-------------------------------+-------------------------+---------------- o(x.). .(..). .(..). .(..).&#x | 1 2 0 0 | 2 0 1 0 0 0 0 0 0 | 2 * * * * * * * * * * * * * | 4 0 0 0 0 0 0 0 0 0 0 0 | 2 2 0 0 0 0 0 0 .(..). o(x.). .(..). .(..).&#x | 1 2 0 0 | 2 0 0 1 0 0 0 0 0 | * 2 * * * * * * * * * * * * | 0 4 0 0 0 0 0 0 0 0 0 0 | 0 0 2 2 0 0 0 0 o(oo). o(oo). o(oo). o(oo).&#x | 1 1 1 0 | 1 1 0 0 1 0 0 0 0 | * * 16 * * * * * * * * * * * | 1 1 1 1 0 0 0 0 0 0 0 0 | 1 1 1 1 0 0 0 0 .(..). .(..). o(.x). .(..).&#x | 1 0 2 0 | 0 2 0 0 0 0 1 0 0 | * * * 2 * * * * * * * * * * | 0 0 4 0 0 0 0 0 0 0 0 0 | 2 0 2 0 0 0 0 0 .(..). .(..). .(..). o(.x).&#x | 1 0 2 0 | 0 2 0 0 0 0 0 1 0 | * * * * 2 * * * * * * * * * | 0 0 0 4 0 0 0 0 0 0 0 0 | 0 2 0 2 0 0 0 0 .(xo). .(..). .(..). .(..).&#x | 0 2 1 0 | 0 0 1 0 2 0 0 0 0 | * * * * * 8 * * * * * * * * | 1 0 0 0 1 1 0 0 1 0 0 0 | 1 1 0 0 1 1 0 0 .(..). .(xo). .(..). .(..).&#x | 0 2 1 0 | 0 0 0 1 2 0 0 0 0 | * * * * * * 8 * * * * * * * | 0 1 0 0 0 0 1 1 0 1 0 0 | 0 0 1 1 0 0 1 1 .(..). .(..). .(ox). .(..).&#x | 0 1 2 0 | 0 0 0 0 2 0 1 0 0 | * * * * * * * 8 * * * * * * | 0 0 1 0 1 0 1 0 0 0 1 0 | 1 0 1 0 1 0 1 0 .(..). .(..). .(..). .(ox).&#x | 0 1 2 0 | 0 0 0 0 2 0 0 1 0 | * * * * * * * * 8 * * * * * | 0 0 0 1 0 1 0 1 0 0 0 1 | 0 1 0 1 0 1 0 1 .(x.)o .(..). .(..). .(..).&#x | 0 2 0 1 | 0 0 1 0 0 2 0 0 0 | * * * * * * * * * 2 * * * * | 0 0 0 0 0 0 0 0 4 0 0 0 | 0 0 0 0 2 2 0 0 .(..). .(x.)o .(..). .(..).&#x | 0 2 0 1 | 0 0 0 1 0 2 0 0 0 | * * * * * * * * * * 2 * * * | 0 0 0 0 0 0 0 0 0 4 0 0 | 0 0 0 0 0 0 2 2 .(oo)o .(oo)o .(oo)o .(oo)o&#x | 0 1 1 1 | 0 0 0 0 1 1 0 0 1 | * * * * * * * * * * * 16 * * | 0 0 0 0 0 0 0 0 1 1 1 1 | 0 0 0 0 1 1 1 1 .(..). .(..). .(.x)o .(..).&#x | 0 0 2 1 | 0 0 0 0 0 0 1 0 2 | * * * * * * * * * * * * 2 * | 0 0 0 0 0 0 0 0 0 0 4 0 | 0 0 0 0 2 0 2 0 .(..). .(..). .(..). .(.x)o&#x | 0 0 2 1 | 0 0 0 0 0 0 0 1 2 | * * * * * * * * * * * * * 2 | 0 0 0 0 0 0 0 0 0 0 0 4 | 0 0 0 0 0 2 0 2 -------------------------------+---------+--------------------+-------------------------------+-------------------------+---------------- o(xo). .(..). .(..). .(..).&#x ♦ 1 2 1 0 | 2 1 1 0 2 0 0 0 0 | 1 0 2 0 0 1 0 0 0 0 0 0 0 0 | 8 * * * * * * * * * * * | 1 1 0 0 0 0 0 0 .(..). o(xo). .(..). .(..).&#x ♦ 1 2 1 0 | 2 1 0 1 2 0 0 0 0 | 0 1 2 0 0 0 1 0 0 0 0 0 0 0 | * 8 * * * * * * * * * * | 0 0 1 1 0 0 0 0 .(..). .(..). o(ox). .(..).&#x ♦ 1 1 2 0 | 1 2 0 0 2 0 1 0 0 | 0 0 2 1 0 0 0 1 0 0 0 0 0 0 | * * 8 * * * * * * * * * | 1 0 1 0 0 0 0 0 .(..). .(..). .(..). o(ox).&#x ♦ 1 1 2 0 | 1 2 0 0 2 0 0 1 0 | 0 0 2 0 1 0 0 0 1 0 0 0 0 0 | * * * 8 * * * * * * * * | 0 1 0 1 0 0 0 0 .(xo). .(..). .(ox). .(..).&#x ♦ 0 2 2 0 | 0 0 1 0 4 0 1 0 0 | 0 0 0 0 0 2 0 2 0 0 0 0 0 0 | * * * * 4 * * * * * * * | 1 0 0 0 1 0 0 0 .(xo). .(..). .(..). .(ox).&#x ♦ 0 2 2 0 | 0 0 1 0 4 0 0 1 0 | 0 0 0 0 0 2 0 0 2 0 0 0 0 0 | * * * * * 4 * * * * * * | 0 1 0 0 0 1 0 0 .(..). .(xo). .(ox). .(..).&#x ♦ 0 2 2 0 | 0 0 0 1 4 0 1 0 0 | 0 0 0 0 0 0 2 2 0 0 0 0 0 0 | * * * * * * 4 * * * * * | 0 0 1 0 0 0 1 0 .(..). .(xo). .(..). .(ox).&#x ♦ 0 2 2 0 | 0 0 0 1 4 0 0 1 0 | 0 0 0 0 0 0 2 0 2 0 0 0 0 0 | * * * * * * * 4 * * * * | 0 0 0 1 0 0 0 1 .(xo)o .(..). .(..). .(..).&#x ♦ 0 2 1 1 | 0 0 1 0 2 2 0 0 1 | 0 0 0 0 0 1 0 0 0 1 0 2 0 0 | * * * * * * * * 8 * * * | 0 0 0 0 1 1 0 0 .(..). .(xo)o .(..). .(..).&#x ♦ 0 2 1 1 | 0 0 0 1 2 2 0 0 1 | 0 0 0 0 0 0 1 0 0 0 1 2 0 0 | * * * * * * * * * 8 * * | 0 0 0 0 0 0 1 1 .(..). .(..). .(ox)o .(..).&#x ♦ 0 1 2 1 | 0 0 0 0 2 1 1 0 2 | 0 0 0 0 0 0 0 1 0 0 0 2 1 0 | * * * * * * * * * * 8 * | 0 0 0 0 1 0 1 0 .(..). .(..). .(..). .(ox)o&#x ♦ 0 1 2 1 | 0 0 0 0 2 1 0 1 2 | 0 0 0 0 0 0 0 0 1 0 0 2 0 1 | * * * * * * * * * * * 8 | 0 0 0 0 0 1 0 1 -------------------------------+---------+--------------------+-------------------------------+-------------------------+---------------- o(xo). .(..). o(ox). .(..).&#x ♦ 1 2 2 0 | 2 2 1 0 4 0 1 0 0 | 1 0 4 1 0 2 0 2 0 0 0 0 0 0 | 2 0 2 0 1 0 0 0 0 0 0 0 | 4 * * * * * * * o(xo). .(..). .(..). o(ox).&#x ♦ 1 2 2 0 | 2 2 1 0 4 0 0 1 0 | 1 0 4 0 1 2 0 0 2 0 0 0 0 0 | 2 0 0 2 0 1 0 0 0 0 0 0 | * 4 * * * * * * .(..). o(xo). o(ox). .(..).&#x ♦ 1 2 2 0 | 2 2 0 1 4 0 1 0 0 | 0 1 4 1 0 0 2 2 0 0 0 0 0 0 | 0 2 2 0 0 0 1 0 0 0 0 0 | * * 4 * * * * * .(..). o(xo). .(..). o(ox).&#x ♦ 1 2 2 0 | 2 2 0 1 4 0 0 1 0 | 0 1 4 0 1 0 2 0 2 0 0 0 0 0 | 0 2 0 2 0 0 0 1 0 0 0 0 | * * * 4 * * * * .(xo)o .(..). .(ox)o .(..).&#x ♦ 0 2 2 1 | 0 0 1 0 4 2 1 0 2 | 0 0 0 0 0 2 0 2 0 1 0 4 1 0 | 0 0 0 0 1 0 0 0 2 0 2 0 | * * * * 4 * * * .(xo)o .(..). .(..). .(ox)o&#x ♦ 0 2 2 1 | 0 0 1 0 4 2 0 1 2 | 0 0 0 0 0 2 0 0 2 1 0 4 0 1 | 0 0 0 0 0 1 0 0 2 0 0 2 | * * * * * 4 * * .(..). .(xo)o .(ox)o .(..).&#x ♦ 0 2 2 1 | 0 0 0 1 4 2 1 0 2 | 0 0 0 0 0 0 2 2 0 0 1 4 1 0 | 0 0 0 0 0 0 1 0 0 2 2 0 | * * * * * * 4 * .(..). .(xo)o .(..). .(ox)o&#x ♦ 0 2 2 1 | 0 0 0 1 4 2 0 1 2 | 0 0 0 0 0 0 2 0 2 0 1 4 0 1 | 0 0 0 0 0 0 0 1 0 2 0 2 | * * * * * * * 4
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