Acronym | scad (old: shad) | |||||||||||||||||||||||||||||||||||||||||||||||||
Name |
small cellated dodecateron, small hedrated dodecateron, stericated hexateron, expanded hexateron, vertex figure of cyxh, lattice A5 contact polytope (span of its roots), equatorial cross-section of hix-first staf, equatorial cross-section of rix-first rag, equatorial cross-section of vertex-first mo | |||||||||||||||||||||||||||||||||||||||||||||||||
Field of sections |
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Circumradius | 1 | |||||||||||||||||||||||||||||||||||||||||||||||||
Inradius wrt. pen | sqrt(3/5) = 0.774597 | |||||||||||||||||||||||||||||||||||||||||||||||||
Inradius wrt. tepe | sqrt(3/8) = 0.612372 | |||||||||||||||||||||||||||||||||||||||||||||||||
Inradius wrt. triddip | 1/sqrt(3) = 0.577350 | |||||||||||||||||||||||||||||||||||||||||||||||||
Vertex figure |
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Lace city in approx. ASCII-art |
o t -- o3o3o3x (pen) T C t -- x3o3o3x (spid) T o -- x3o3o3o (dual pen) \ \ +-- x x3o3o (tepe) \ +------- uo ox3oo3ox +------------ x o3o3x (inv. tepe) where: o - o3o3o (point) t - x3o3o (tet) C - x3o3x (co) T - o3o3x (dual tet) | |||||||||||||||||||||||||||||||||||||||||||||||||
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Lace hyper city in approx. ASCII-art |
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Volume | 21 sqrt(3)/40 = 0.909327 | |||||||||||||||||||||||||||||||||||||||||||||||||
Surface | (30+20 sqrt(2)+sqrt(5))/8 = 7.565042 | |||||||||||||||||||||||||||||||||||||||||||||||||
General of army | (is itself convex) | |||||||||||||||||||||||||||||||||||||||||||||||||
Colonel of regiment |
(is itself locally convex
– uniform polyteral members:
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Dihedral angles
(at margins) | ||||||||||||||||||||||||||||||||||||||||||||||||||
Face vector | 30, 120, 210, 180, 62 | |||||||||||||||||||||||||||||||||||||||||||||||||
Confer |
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External links |
By virtue of an outer symmetry this is a non-quasiregular monotoxal polyteron, that is all edges belong to the same equivalence class.
Incidence matrix according to Dynkin symbol
x3o3o3o3x . . . . . | 30 ♦ 4 4 | 6 12 6 | 4 12 12 4 | 1 4 6 4 1 ----------+----+-------+----------+-------------+------------- x . . . . | 2 | 60 * | 3 3 0 | 3 6 3 0 | 1 3 3 1 0 . . . . x | 2 | * 60 | 0 3 3 | 0 3 6 3 | 0 1 3 3 1 ----------+----+-------+----------+-------------+------------- x3o . . . | 3 | 3 0 | 60 * * | 2 2 0 0 | 1 2 1 0 0 x . . . x | 4 | 2 2 | * 90 * | 0 2 2 0 | 0 1 2 1 0 . . . o3x | 3 | 0 3 | * * 60 | 0 0 2 2 | 0 0 1 2 1 ----------+----+-------+----------+-------------+------------- x3o3o . . ♦ 4 | 6 0 | 4 0 0 | 30 * * * | 1 1 0 0 0 x3o . . x ♦ 6 | 6 3 | 2 3 0 | * 60 * * | 0 1 1 0 0 x . . o3x ♦ 6 | 3 6 | 0 3 2 | * * 60 * | 0 0 1 1 0 . . o3o3x ♦ 4 | 0 6 | 0 0 4 | * * * 30 | 0 0 0 1 1 ----------+----+-------+----------+-------------+------------- x3o3o3o . ♦ 5 | 10 0 | 10 0 0 | 5 0 0 0 | 6 * * * * x3o3o . x ♦ 8 | 12 4 | 8 6 0 | 2 4 0 0 | * 15 * * * x3o . o3x ♦ 9 | 9 9 | 3 9 3 | 0 3 3 0 | * * 20 * * x . o3o3x ♦ 8 | 4 12 | 0 6 8 | 0 0 4 2 | * * * 15 * . o3o3o3x ♦ 5 | 0 10 | 0 0 10 | 0 0 0 5 | * * * * 6
or . . . . . | 30 ♦ 8 | 12 12 | 8 24 | 2 8 6 -------------+----+-----+--------+--------+--------- x . . . . & | 2 | 120 | 3 3 | 3 9 | 1 4 3 -------------+----+-----+--------+--------+--------- x3o . . . & | 3 | 3 | 120 * | 2 2 | 1 2 1 x . . . x | 4 | 4 | * 90 | 0 4 | 0 2 2 -------------+----+-----+--------+--------+--------- x3o3o . . & ♦ 4 | 6 | 4 0 | 60 * | 1 1 0 x3o . . x & ♦ 6 | 9 | 2 3 | * 120 | 0 1 1 -------------+----+-----+--------+--------+--------- x3o3o3o . & ♦ 5 | 10 | 10 0 | 5 0 | 12 * * x3o3o . x & ♦ 8 | 16 | 8 6 | 2 4 | * 30 * x3o . o3x ♦ 9 | 18 | 6 9 | 0 6 | * * 20
xxo3ooo3ooo3oxx&#xt → both heights = sqrt(3/5) = 0.774597 (pen || pseudo spid || dual pen) o..3o..3o..3o.. | 5 * * ♦ 4 4 0 0 0 0 | 6 12 6 0 0 0 0 0 0 | 4 12 12 4 0 0 0 0 0 0 0 0 | 1 4 6 4 1 0 0 0 0 0 .o.3.o.3.o.3.o. | * 20 * ♦ 0 1 3 3 1 0 | 0 3 3 3 6 3 3 3 0 | 0 3 6 3 1 3 3 1 3 6 3 0 | 0 1 3 3 1 1 3 3 1 0 ..o3..o3..o3..o | * * 5 ♦ 0 0 0 0 4 4 | 0 0 0 0 0 0 6 12 6 | 0 0 0 0 0 0 0 0 4 12 12 4 | 0 0 0 0 0 1 4 6 4 1 -------------------+--------+-------------------+----------------------------+---------------------------------+------------------------ x.. ... ... ... | 2 0 0 | 10 * * * * * | 3 3 0 0 0 0 0 0 0 | 3 6 3 0 0 0 0 0 0 0 0 0 | 1 3 3 1 0 0 0 0 0 0 oo.3oo.3oo.3oo.&#x | 1 1 0 | * 20 * * * * | 0 3 3 0 0 0 0 0 0 | 0 3 6 3 0 0 0 0 0 0 0 0 | 0 1 3 3 1 0 0 0 0 0 .x. ... ... ... | 0 2 0 | * * 30 * * * | 0 1 0 2 2 0 1 0 0 | 0 2 2 0 1 2 1 0 2 2 0 0 | 0 1 2 1 0 1 2 1 0 0 ... ... ... .x. | 0 2 0 | * * * 30 * * | 0 0 1 0 2 2 0 1 0 | 0 0 2 2 0 1 2 1 0 2 2 0 | 0 0 1 2 1 0 1 2 1 0 .oo3.oo3.oo3.oo&#x | 0 1 1 | * * * * 20 * | 0 0 0 0 0 0 3 3 0 | 0 0 0 0 0 0 0 0 3 6 3 0 | 0 0 0 0 0 1 3 3 1 0 ... ... ... ..x | 0 0 2 | * * * * * 10 | 0 0 0 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 0 3 6 3 | 0 0 0 0 0 0 1 3 3 1 -------------------+--------+-------------------+----------------------------+---------------------------------+------------------------ x..3o.. ... ... | 3 0 0 | 3 0 0 0 0 0 | 10 * * * * * * * * | 2 2 0 0 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 0 0 0 xx. ... ... ...&#x | 2 2 0 | 1 2 1 0 0 0 | * 30 * * * * * * * | 0 2 2 0 0 0 0 0 0 0 0 0 | 0 1 2 1 0 0 0 0 0 0 ... ... ... ox.&#x | 1 2 0 | 0 2 0 1 0 0 | * * 30 * * * * * * | 0 0 2 2 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 3 0 0 0 | * * * 20 * * * * * | 0 1 0 0 1 1 0 0 1 0 0 0 | 0 1 1 0 0 1 1 0 0 0 .x. ... ... .x. | 0 4 0 | 0 0 2 2 0 0 | * * * * 30 * * * * | 0 0 1 0 0 1 1 0 0 1 0 0 | 0 0 1 1 0 0 1 1 0 0 ... ... .o.3.x. | 0 3 0 | 0 0 0 3 0 0 | * * * * * 20 * * * | 0 0 0 1 0 0 1 1 0 0 1 0 | 0 0 0 1 1 0 0 1 1 0 .xo ... ... ...&#x | 0 2 1 | 0 0 1 0 2 0 | * * * * * * 30 * * | 0 0 0 0 0 0 0 0 2 2 0 0 | 0 0 0 0 0 1 2 1 0 0 ... ... ... .xx&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * * * * 30 * | 0 0 0 0 0 0 0 0 0 2 2 0 | 0 0 0 0 0 0 1 2 1 0 ... ... ..o3..x | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * 10 | 0 0 0 0 0 0 0 0 0 0 2 2 | 0 0 0 0 0 0 0 1 2 1 -------------------+--------+-------------------+----------------------------+---------------------------------+------------------------ x..3o..3o.. ... ♦ 4 0 0 | 6 0 0 0 0 0 | 4 0 0 0 0 0 0 0 0 | 5 * * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 0 xx.3oo. ... ...&#x ♦ 3 3 0 | 3 3 3 0 0 0 | 1 3 0 1 0 0 0 0 0 | * 20 * * * * * * * * * * | 0 1 1 0 0 0 0 0 0 0 xx. ... ... ox.&#x ♦ 2 4 0 | 1 4 2 2 0 0 | 0 2 2 0 1 0 0 0 0 | * * 30 * * * * * * * * * | 0 0 1 1 0 0 0 0 0 0 ... ... oo.3ox.&#x ♦ 1 3 0 | 0 3 0 3 0 0 | 0 0 3 0 0 1 0 0 0 | * * * 20 * * * * * * * * | 0 0 0 1 1 0 0 0 0 0 .x.3.o.3.o. ... ♦ 0 4 0 | 0 0 6 0 0 0 | 0 0 0 4 0 0 0 0 0 | * * * * 5 * * * * * * * | 0 1 0 0 0 1 0 0 0 0 .x.3.o. ... .x. ♦ 0 6 0 | 0 0 6 3 0 0 | 0 0 0 2 3 0 0 0 0 | * * * * * 10 * * * * * * | 0 0 1 0 0 0 1 0 0 0 .x. ... .o.3.x. ♦ 0 6 0 | 0 0 3 6 0 0 | 0 0 0 0 3 2 0 0 0 | * * * * * * 10 * * * * * | 0 0 0 1 0 0 0 1 0 0 ... .o.3.o.3.x. ♦ 0 4 0 | 0 0 0 6 0 0 | 0 0 0 0 0 4 0 0 0 | * * * * * * * 5 * * * * | 0 0 0 0 1 0 0 0 1 0 .xo3.oo ... ...&#x ♦ 0 3 1 | 0 0 3 0 3 0 | 0 0 0 1 0 0 3 0 0 | * * * * * * * * 20 * * * | 0 0 0 0 0 1 1 0 0 0 .xo ... ... .xx&#x ♦ 0 4 2 | 0 0 2 2 4 1 | 0 0 0 0 1 0 2 2 0 | * * * * * * * * * 30 * * | 0 0 0 0 0 0 1 1 0 0 ... ... .oo3.xx&#x ♦ 0 3 3 | 0 0 0 3 3 3 | 0 0 0 0 0 1 0 3 1 | * * * * * * * * * * 20 * | 0 0 0 0 0 0 0 1 1 0 ... ..o3..o3..x ♦ 0 0 4 | 0 0 0 0 0 6 | 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * 5 | 0 0 0 0 0 0 0 0 1 1 -------------------+--------+-------------------+----------------------------+---------------------------------+------------------------ x..3o..3o..3o.. ♦ 5 0 0 | 10 0 0 0 0 0 | 10 0 0 0 0 0 0 0 0 | 5 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * xx.3oo.3oo. ...&#x ♦ 4 4 0 | 6 4 6 0 0 0 | 4 6 0 4 0 0 0 0 0 | 1 4 0 0 1 0 0 0 0 0 0 0 | * 5 * * * * * * * * xx.3oo. ... ox.&#x ♦ 3 6 0 | 3 6 6 3 0 0 | 1 6 3 2 3 0 0 0 0 | 0 2 3 0 0 1 0 0 0 0 0 0 | * * 10 * * * * * * * xx. ... oo.3ox.&#x ♦ 2 6 0 | 1 6 3 6 0 0 | 0 3 6 0 3 2 0 0 0 | 0 0 3 2 0 0 1 0 0 0 0 0 | * * * 10 * * * * * * ... oo.3oo.3ox.&#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 | * * * * 5 * * * * * .xo3.oo3.oo ...&#x ♦ 0 4 1 | 0 0 6 0 4 0 | 0 0 0 4 0 0 6 0 0 | 0 0 0 0 1 0 0 0 4 0 0 0 | * * * * * 5 * * * * .xo3.oo ... .xx&#x ♦ 0 6 2 | 0 0 6 3 6 1 | 0 0 0 2 3 0 6 3 0 | 0 0 0 0 0 1 0 0 2 3 0 0 | * * * * * * 10 * * * .xo ... .oo3.xx&#x ♦ 0 6 3 | 0 0 3 6 6 3 | 0 0 0 0 3 2 3 6 1 | 0 0 0 0 0 0 1 0 0 3 2 0 | * * * * * * * 10 * * ... .oo3.oo3.xx&#x ♦ 0 4 4 | 0 0 0 6 4 6 | 0 0 0 0 0 4 0 6 4 | 0 0 0 0 0 0 0 1 0 0 4 1 | * * * * * * * * 5 * ..o3..o3..o3..x ♦ 0 0 5 | 0 0 0 0 0 10 | 0 0 0 0 0 0 0 0 10 | 0 0 0 0 0 0 0 0 0 0 0 5 | * * * * * * * * * 1
or o..3o..3o..3o.. & | 10 * ♦ 4 4 0 | 6 12 6 0 0 | 4 12 12 4 0 0 | 1 4 6 4 1 .o.3.o.3.o.3.o. | * 20 ♦ 0 2 6 | 0 6 6 6 6 | 0 6 12 6 2 6 | 0 2 6 6 2 ---------------------+-------+----------+----------------+-------------------+-------------- x.. ... ... ... & | 2 0 | 20 * * | 3 3 0 0 0 | 3 6 3 0 0 0 | 1 3 3 1 0 oo.3oo.3oo.3oo.&#x & | 1 1 | * 40 * | 0 3 3 0 0 | 0 3 6 3 0 0 | 0 1 3 3 1 .x. ... ... ... & | 0 2 | * * 60 | 0 1 1 2 2 | 0 2 4 2 1 3 | 0 1 3 3 1 ---------------------+-------+----------+----------------+-------------------+-------------- x..3o.. ... ... & | 3 0 | 3 0 0 | 20 * * * * | 2 2 0 0 0 0 | 1 2 1 0 0 xx. ... ... ...&#x & | 2 2 | 1 2 1 | * 60 * * * | 0 2 2 0 0 0 | 0 1 2 1 0 ... ... ... ox.&#x & | 1 2 | 0 2 1 | * * 60 * * | 0 0 2 2 0 0 | 0 0 1 2 1 .x.3.o. ... ... & | 0 3 | 0 0 3 | * * * 40 * | 0 1 0 1 1 1 | 0 1 1 1 1 .x. ... ... .x. | 0 4 | 0 0 4 | * * * * 30 | 0 0 2 0 0 2 | 0 0 2 2 0 ---------------------+-------+----------+----------------+-------------------+-------------- x..3o..3o.. ... & ♦ 4 0 | 6 0 0 | 4 0 0 0 0 | 10 * * * * * | 1 1 0 0 0 xx.3oo. ... ...&#x & ♦ 3 3 | 3 3 3 | 1 3 0 1 0 | * 40 * * * * | 0 1 1 0 0 xx. ... ... ox.&#x & ♦ 2 4 | 1 4 4 | 0 2 2 0 1 | * * 60 * * * | 0 0 1 1 0 ... ... oo.3ox.&#x & ♦ 1 3 | 0 3 3 | 0 0 3 1 0 | * * * 40 * * | 0 0 0 1 1 .x.3.o.3.o. ... & ♦ 0 4 | 0 0 6 | 0 0 0 4 0 | * * * * 10 * | 0 1 0 0 1 .x.3.o. ... .x. & ♦ 0 6 | 0 0 9 | 0 0 0 2 3 | * * * * * 20 | 0 0 1 1 0 ---------------------+-------+----------+----------------+-------------------+-------------- x..3o..3o..3o.. & ♦ 5 0 | 10 0 0 | 10 0 0 0 0 | 5 0 0 0 0 0 | 2 * * * * xx.3oo.3oo. ...&#x & ♦ 4 4 | 6 4 6 | 4 6 0 4 0 | 1 4 0 0 1 0 | * 10 * * * xx.3oo. ... ox.&#x & ♦ 3 6 | 3 6 9 | 1 6 3 2 3 | 0 2 3 0 0 1 | * * 20 * * xx. ... oo.3ox.&#x & ♦ 2 6 | 1 6 9 | 0 3 6 2 3 | 0 0 3 2 0 1 | * * * 20 * ... oo.3oo.3ox.&#x & ♦ 1 4 | 0 4 6 | 0 0 6 4 0 | 0 0 0 4 1 0 | * * * * 10
x(xo)o3o(xo)x x(ox)o3o(ox)x&#xt → all heights = 1/sqrt(3) = 0.577350 (triddip || pseudo ({6} x pt, pt x {6})-compound † || bi-inv triddip) o(..).3o(..). o(..).3o(..). & | 18 * ♦ 2 2 2 2 0 0 | 1 4 1 2 1 4 4 2 1 4 | 2 2 4 2 2 2 4 2 6 6 | 1 2 1 2 1 5 2 2 .(o.).3.(o.). .(o.).3.(o.). & | * 12 ♦ 0 0 3 3 1 1 | 0 0 0 3 3 3 3 3 3 6 | 0 0 3 3 1 1 3 3 9 9 | 0 1 1 1 1 6 3 3 ----------------------------------+-------+-----------------+-----------------------------+-----------------------------+----------------- x(..). .(..). .(..). .(..). & | 2 0 | 18 * * * * * | 1 2 0 1 0 0 2 0 0 0 | 2 1 2 0 0 2 2 1 2 0 | 1 1 0 2 1 2 1 0 .(..). .(..). x(..). .(..). & | 2 0 | * 18 * * * * | 0 2 1 0 0 2 0 1 0 0 | 1 2 2 1 2 0 2 0 0 2 | 1 2 1 1 0 2 0 1 o(o.).3o(o.). o(o.).3o(o.).&#x & | 1 1 | * * 36 * * * | 0 0 0 1 1 2 0 0 0 2 | 0 0 2 2 1 0 0 0 3 4 | 0 1 1 0 0 3 1 2 o(.o).3o(.o). o(.o).3o(.o).&#x & | 1 1 | * * * 36 * * | 0 0 0 0 0 0 2 1 1 2 | 0 0 0 0 0 1 2 2 4 3 | 0 0 0 1 1 3 2 1 .(x.). .(..). .(..). .(..). & | 0 2 | * * * * 6 * | 0 0 0 3 0 0 0 0 3 0 | 0 0 3 0 0 0 0 3 6 0 | 0 1 0 0 1 3 3 0 .(..). .(x.). .(..). .(..). & | 0 2 | * * * * * 6 | 0 0 0 0 3 0 0 3 0 0 | 0 0 0 3 0 0 3 0 0 6 | 0 0 1 1 0 3 0 3 ----------------------------------+-------+-----------------+-----------------------------+-----------------------------+----------------- x(..).3o(..). .(..). .(..). & | 3 0 | 3 0 0 0 0 0 | 6 * * * * * * * * * | 2 0 0 0 0 2 0 0 0 0 | 1 0 0 2 1 0 0 0 x(..). .(..). x(..). .(..). & | 4 0 | 2 2 0 0 0 0 | * 18 * * * * * * * * | 1 1 1 0 0 0 1 0 0 0 | 1 1 0 1 0 1 0 0 .(..). .(..). x(..).3o(..). & | 3 0 | 0 3 0 0 0 0 | * * 6 * * * * * * * | 0 2 0 0 2 0 0 0 0 0 | 1 2 1 0 0 0 0 0 x(x.). .(..). .(..). .(..).&#x & | 2 2 | 1 0 2 0 1 0 | * * * 18 * * * * * * | 0 0 2 0 0 0 0 0 2 0 | 0 1 0 0 0 2 1 0 .(..). o(x.). .(..). .(..).&#x & | 1 2 | 0 0 2 0 0 1 | * * * * 18 * * * * * | 0 0 0 2 0 0 0 0 0 2 | 0 0 1 0 0 1 0 2 .(..). .(..). x(o.). .(..).&#x & | 2 1 | 0 1 2 0 0 0 | * * * * * 36 * * * * | 0 0 1 1 1 0 0 0 0 1 | 0 1 1 0 0 1 0 1 x(.o). .(..). .(..). .(..).&#x & | 2 1 | 1 0 0 2 0 0 | * * * * * * 36 * * * | 0 0 0 0 0 1 1 1 1 0 | 0 0 0 1 1 1 1 0 .(..). .(..). x(.x). .(..).&#x & | 2 2 | 0 1 0 2 0 1 | * * * * * * * 18 * * | 0 0 0 0 0 0 2 0 0 2 | 0 0 0 1 0 2 0 1 .(..). .(..). .(..). o(.x).&#x & | 1 2 | 0 0 0 2 1 0 | * * * * * * * * 18 * | 0 0 0 0 0 0 0 2 2 0 | 0 0 0 0 1 1 2 0 o(oo)o o(oo)o o(oo)o o(oo)o&#xr | 2 2 | 0 0 2 2 0 0 | * * * * * * * * * 36 | 0 0 0 0 0 0 0 0 2 2 | 0 0 0 0 0 2 1 1 ----------------------------------+-------+-----------------+-----------------------------+-----------------------------+----------------- x(..).3o(..). x(..). .(..). & ♦ 6 0 | 6 3 0 0 0 0 | 2 3 0 0 0 0 0 0 0 0 | 6 * * * * * * * * * | 1 0 0 1 0 0 0 0 x(..). .(..). x(..).3o(..). & ♦ 6 0 | 3 6 0 0 0 0 | 0 3 2 0 0 0 0 0 0 0 | * 6 * * * * * * * * | 1 1 0 0 0 0 0 0 x(x.). .(..). x(o.). .(..).&#x & ♦ 4 2 | 2 2 4 0 1 0 | 0 1 0 2 0 2 0 0 0 0 | * * 18 * * * * * * * | 0 1 0 0 0 1 0 0 .(..). o(x.). x(o.). .(..).&#x & ♦ 2 2 | 0 1 4 0 0 1 | 0 0 0 0 2 2 0 0 0 0 | * * * 18 * * * * * * | 0 0 1 0 0 0 0 1 .(..). .(..). x(o.).3o(o.).&#x & ♦ 3 1 | 0 3 3 0 0 0 | 0 0 1 0 0 3 0 0 0 0 | * * * * 12 * * * * * | 0 1 1 0 0 0 0 0 x(.o).3o(.o). .(..). .(..).&#x & ♦ 3 1 | 3 0 0 3 0 0 | 1 0 0 0 0 0 3 0 0 0 | * * * * * 12 * * * * | 0 0 0 1 1 0 0 0 x(.o). .(..). x(.x). .(..).&#x & ♦ 4 2 | 2 2 0 4 0 1 | 0 1 0 0 0 0 2 2 0 0 | * * * * * * 18 * * * | 0 0 0 1 0 1 0 0 x(.o). .(..). .(..). o(.x).&#x & ♦ 2 2 | 1 0 0 4 1 0 | 0 0 0 0 0 0 2 0 2 0 | * * * * * * * 18 * * | 0 0 0 0 1 0 1 0 x(xo)o .(..). .(..). .(..).&#xr & ♦ 3 3 | 1 0 3 4 1 0 | 0 0 0 1 0 0 1 0 1 2 | * * * * * * * * 36 * | 0 0 0 0 0 1 1 0 .(..). o(xo)x .(..). .(..).&#xr & ♦ 3 3 | 0 1 4 3 0 1 | 0 0 0 0 1 1 0 1 0 2 | * * * * * * * * * 36 | 0 0 0 0 0 1 0 1 ----------------------------------+-------+-----------------+-----------------------------+-----------------------------+----------------- x(..).3o(..). x(..).3o(..). & ♦ 9 0 | 9 9 0 0 0 0 | 3 9 3 0 0 0 0 0 0 0 | 3 3 0 0 0 0 0 0 0 0 | 2 * * * * * * * x(x.). .(..). x(o.).3o(o.).&#x & ♦ 6 2 | 3 6 6 0 1 0 | 0 3 2 3 0 6 0 0 0 0 | 0 1 3 0 2 0 0 0 0 0 | * 6 * * * * * * .(..). o(x.). x(o.).3o(o.).&#x & ♦ 3 2 | 0 3 6 0 0 1 | 0 0 1 0 3 6 0 0 0 0 | 0 0 0 3 2 0 0 0 0 0 | * * 6 * * * * * x(.o).3o(.o). x(.x). .(..).&#x & ♦ 6 2 | 6 3 0 6 0 1 | 2 3 0 0 0 0 6 3 0 0 | 1 0 0 0 0 2 3 0 0 0 | * * * 6 * * * * x(.o).3o(.o). .(..). o(.x).&#x & ♦ 3 2 | 3 0 0 6 1 0 | 1 0 0 0 0 0 6 0 3 0 | 0 0 0 0 0 2 0 3 0 0 | * * * * 6 * * * x(xo)o .(..). x(ox)o .(..).&#xr & ♦ 5 4 | 2 2 6 6 1 1 | 0 1 0 2 1 2 2 2 1 4 | 0 0 1 0 0 0 1 0 2 2 | * * * * * 18 * * x(xo)o .(..). .(..). o(ox)x&#xr ♦ 4 4 | 2 0 4 8 2 0 | 0 0 0 2 0 0 4 0 4 4 | 0 0 0 0 0 0 0 2 4 0 | * * * * * * 9 * .(..). o(xo)x x(ox)o .(..).&#xr ♦ 4 4 | 0 2 8 4 0 2 | 0 0 0 0 4 4 0 2 0 4 | 0 0 0 2 0 0 0 0 0 4 | * * * * * * * 9 † – the hull of that compound could be used here instead; that is the bihexagonal tegum xo3xo ox3ox&#zq, the tegum product of 2 x3x.
x(uo)x x(ox)o3o(oo)o3o(ox)x&#xt → both heights = sqrt(3/8) = 0.612372 (tepe || pseudo (u-line, perp co)-compound † || inv tepe) o(..). o(..).3o(..).3o(..). & | 16 * * ♦ 1 3 1 3 0 | 3 3 3 3 6 3 3 0 0 | 3 1 3 6 3 3 3 1 9 | 1 1 3 3 1 4 3 .(o.). .(o.).3.(o.).3.(o.). | * 2 * ♦ 0 0 8 0 0 | 0 0 12 0 0 0 12 0 0 | 0 0 8 0 0 0 0 0 24 | 0 2 0 0 0 8 6 .(.o). .(.o).3.(.o).3.(.o). | * * 12 ♦ 0 0 0 4 4 | 0 0 0 2 8 8 2 2 2 | 0 0 0 4 4 4 8 4 8 | 0 0 2 4 2 4 4 ----------------------------------+---------+---------------+--------------------------+--------------------------+----------------- x(..). .(..). .(..). .(..). & | 2 0 0 | 8 * * * * | 3 0 0 3 0 0 0 0 0 | 3 0 0 6 3 0 0 0 0 | 1 0 3 3 1 0 0 .(..). x(..). .(..). .(..). & | 2 0 0 | * 24 * * * | 1 2 1 0 2 0 0 0 0 | 2 1 2 2 0 2 1 0 2 | 1 1 2 1 0 2 1 o(o.). o(o.).3o(o.).3o(o.).&#x & | 1 1 0 | * * 16 * * | 0 0 3 0 0 0 3 0 0 | 0 0 3 0 0 0 0 0 9 | 0 1 0 0 0 4 3 o(.o). o(.o).3o(.o).3o(.o).&#x & | 1 0 1 | * * * 48 * | 0 0 0 1 2 2 1 0 0 | 0 0 0 2 2 1 2 1 4 | 0 0 1 2 1 2 2 .(..). .(.x). .(..). .(..). & | 0 0 2 | * * * * 24 | 0 0 0 0 2 2 0 1 1 | 0 0 0 1 1 2 4 2 2 | 0 0 1 2 1 2 2 ----------------------------------+---------+---------------+--------------------------+--------------------------+----------------- x(..). x(..). .(..). .(..). & | 4 0 0 | 2 2 0 0 0 | 12 * * * * * * * * | 2 0 0 2 0 0 0 0 0 | 1 0 2 1 0 0 0 .(..). x(..).3o(..). .(..). & | 3 0 0 | 0 3 0 0 0 | * 16 * * * * * * * | 1 1 1 0 0 1 0 0 0 | 1 1 1 0 0 1 0 .(..). x(o.). .(..). .(..).&#x & | 2 1 0 | 0 1 2 0 0 | * * 24 * * * * * * | 0 0 2 0 0 0 0 0 2 | 0 1 0 0 0 2 1 x(.o). .(..). .(..). .(..).&#x & | 2 0 1 | 1 0 0 2 0 | * * * 24 * * * * * | 0 0 0 2 2 0 0 0 0 | 0 0 1 2 1 0 0 .(..). x(.x). .(..). .(..).&#x & | 2 0 2 | 0 1 0 2 1 | * * * * 48 * * * * | 0 0 0 1 0 1 1 0 1 | 0 0 1 1 0 1 1 .(..). .(..). .(..). o(.x).&#x & | 1 0 2 | 0 0 0 2 1 | * * * * * 48 * * * | 0 0 0 0 1 0 1 1 1 | 0 0 0 1 1 1 1 o(oo)o o(oo)o3o(oo)o3o(oo)o&#xt | 2 1 1 | 0 0 2 2 0 | * * * * * * 24 * * | 0 0 0 0 0 0 0 0 4 | 0 0 0 0 0 2 2 .(..). .(.x).3.(.o). .(..). & | 0 0 3 | 0 0 0 0 3 | * * * * * * * 8 * | 0 0 0 0 0 2 0 2 0 | 0 0 1 0 1 2 0 .(..). .(.x). .(..). .(.x). | 0 0 4 | 0 0 0 0 4 | * * * * * * * * 6 | 0 0 0 0 0 0 4 0 0 | 0 0 0 2 0 0 2 ----------------------------------+---------+---------------+--------------------------+--------------------------+----------------- x(..). x(..).3o(..). .(..). & ♦ 6 0 0 | 3 6 0 0 0 | 3 2 0 0 0 0 0 0 0 | 8 * * * * * * * * | 1 0 1 0 0 0 0 .(..). x(..).3o(..).3o(..). & ♦ 4 0 0 | 0 6 0 0 0 | 0 4 0 0 0 0 0 0 0 | * 4 * * * * * * * | 1 1 0 0 0 0 0 .(..). x(o.).3o(o.). .(..).&#x & ♦ 3 1 0 | 0 3 3 0 0 | 0 1 3 0 0 0 0 0 0 | * * 16 * * * * * * | 0 1 0 0 0 1 0 x(.o). x(.x). .(..). .(..).&#x & ♦ 4 0 2 | 2 2 0 4 1 | 1 0 0 2 2 0 0 0 0 | * * * 24 * * * * * | 0 0 1 1 0 0 0 x(.o). .(..). .(..). o(.x).&#x & ♦ 2 0 2 | 1 0 0 4 1 | 0 0 0 2 0 2 0 0 0 | * * * * 24 * * * * | 0 0 0 1 1 0 0 .(..). x(.x).3o(.o). .(..).&#x & ♦ 3 0 3 | 0 3 0 3 3 | 0 1 0 0 3 0 0 1 0 | * * * * * 16 * * * | 0 0 1 0 0 1 0 .(..). x(.x). .(..). o(.x).&#x & ♦ 2 0 4 | 0 1 0 4 4 | 0 0 0 0 2 2 0 0 1 | * * * * * * 24 * * | 0 0 0 1 0 0 1 .(..). .(..). o(.o).3o(.x).&#x & ♦ 1 0 3 | 0 0 0 3 3 | 0 0 0 0 0 3 0 1 0 | * * * * * * * 16 * | 0 0 0 0 1 1 0 .(..). x(ox)o .(..). .(..).&#xt & ♦ 3 1 2 | 0 1 3 4 1 | 0 0 1 0 1 1 2 0 0 | * * * * * * * * 48 | 0 0 0 0 0 1 1 ----------------------------------+---------+---------------+--------------------------+--------------------------+----------------- x(..). x(..).3o(..).3o(..). & ♦ 8 0 0 | 4 12 0 0 0 | 6 8 0 0 0 0 0 0 0 | 4 2 0 0 0 0 0 0 0 | 2 * * * * * * .(..). x(o.).3o(o.).3o(o.).&#x & ♦ 4 1 0 | 0 6 4 0 0 | 0 4 6 0 0 0 0 0 0 | 0 1 4 0 0 0 0 0 0 | * 4 * * * * * x(.o). x(.x).3o(.o). .(..).&#x & ♦ 6 0 3 | 3 6 0 6 3 | 3 2 0 3 6 0 0 1 0 | 1 0 0 3 0 2 0 0 0 | * * 8 * * * * x(.o). x(.x). .(..). o(.x).&#x & ♦ 4 0 4 | 2 2 0 8 4 | 1 0 0 4 4 4 0 0 1 | 0 0 0 2 2 0 2 0 0 | * * * 12 * * * x(.o). .(..). o(.o).3o(.x).&#x & ♦ 2 0 3 | 1 0 0 6 3 | 0 0 0 3 0 6 0 1 0 | 0 0 0 0 3 0 0 2 0 | * * * * 8 * * .(..). x(ox)o3o(oo)o .(..).&#xt & ♦ 4 1 3 | 0 3 4 6 3 | 0 1 3 0 3 3 3 1 0 | 0 0 1 0 0 1 0 1 3 | * * * * * 16 * .(..). x(ox)o .(..). o(ox)x&#xt ♦ 4 1 4 | 0 2 4 8 4 | 0 0 2 0 4 4 4 0 1 | 0 0 0 0 0 0 2 0 4 | * * * * * * 12 † – the hull of that compound could be used here instead; that is the tegum uo ox3oo3ox&#zq, the tegum product of u-line and co
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