Acronym | jak (old: yaz) | |||||||||||||||||||||||||
Name |
icosiheptaheptacontidipeton, argyropeton, sideropeton, Gosset polypeton 22,1, vertex figure of naq, Delone cell of lattice E6 | |||||||||||||||||||||||||
Circumradius | sqrt(2/3) = 0.816497 | |||||||||||||||||||||||||
Inradius wrt. hix | 1/2 = 0.5 | |||||||||||||||||||||||||
Inradius wrt. tac | 1/sqrt(6) = 0.408248 | |||||||||||||||||||||||||
Lace city in approx. ASCII-art |
p where: E X = x3o3o *b3o ("normal" hex) X p E = o3o3x *b3o ("even" hex) O O = o3o3o *b3x ("odd" hex) p p = o3o3o *b3o (point) | | + o3o3o *b3o3o (point) | +---- x3o3o *b3o3o (hin) +-------- o3o3o *b3o3x (tac) | |||||||||||||||||||||||||
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o p -- x3o3o3o3o (hix) r d -- o3o3o3x3o (inv rix) o p -- x3o3o3o3o (hix) \ \ \ \ \ +-- o3o3o *b3o3x (tac) \ +---- x3o3o *b3o3o (hin) +------ o3o3o *b3o3o (point) where: o = o3o3o3o (point) p = x3o3o3o (pen) d = o3o3o3x (dual pen) r = o3o3x3o (inv rap) | ||||||||||||||||||||||||||
+------------ o3o3o *b3o3x (tac) | +------- x3o3o *b3o3o (hin) | | +-- o3o3o *b3o3o (point) l t -- x3o3o3o3o (hix) o T p -- o3o3o3x3o (inv rix) l t -- x3o3o3o3o (hix) \_ \_ \_ +-- o x3o3o3o (pen) \_ \_ +---- x o3o3o3x (inv penp) \_ +------ o o3x3o3o (rap) +-------- x o3o3o3o (line) where: l = x o3o3o (line) o = o o3x3o (oct) t = o x3o3o (tet) T = x o3o3x (inv tepe) p = o o3o3o (point) | ||||||||||||||||||||||||||
Coordinates |
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Volume | sqrt(3)/16 = 0.108253 | |||||||||||||||||||||||||
Surface | [18 sqrt(2)+3 sqrt(3)]/20 = 1.532600 | |||||||||||||||||||||||||
Dihedral angles
(at margins) | ||||||||||||||||||||||||||
General of army | (is itself convex) | |||||||||||||||||||||||||
Colonel of regiment |
(is itself locally convex
– uniform polypetal members:
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Face vector | 27, 216, 720, 1080, 648, 99 | |||||||||||||||||||||||||
Confer |
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External links |
It should be noted that the reduction of the inscribed rap from the third lace city representation still allows for a further orbiform diminishing, dedjak, in addition to all the above already mentioned segmentotopes. That one is easily seen to be nothing but the axial stack of penaf and hixip. However, as can be seen from the last lace city, that external blend would be concave only.
Wrt. A5 × A1 subsymmetry jak can be thought of as a tegum sum of hixip
and inv. rix.
Wrt. A2 × A2 × A2 subsymmetry jak can be thought of as a tegum sum of
3 mutually gyro-orthogonal triddips.
From the above high symmetrical vertex subsets by combination further at least orbiform vertex inscribed polytopes are derivable:
Incidence matrix according to Dynkin symbol
x3o3o3o3o *c3o . . . . . . | 27 ♦ 16 | 80 | 160 | 80 40 | 16 10 ---------------+----+-----+-----+------+---------+------ x . . . . . | 2 | 216 ♦ 10 | 30 | 20 10 | 5 5 ---------------+----+-----+-----+------+---------+------ x3o . . . . | 3 | 3 | 720 ♦ 6 | 6 3 | 2 3 ---------------+----+-----+-----+------+---------+------ x3o3o . . . ♦ 4 | 6 | 4 | 1080 | 2 1 | 1 2 ---------------+----+-----+-----+------+---------+------ x3o3o3o . . ♦ 5 | 10 | 10 | 5 | 432 * | 1 1 x3o3o . . *c3o ♦ 5 | 10 | 10 | 5 | * 216 | 0 2 ---------------+----+-----+-----+------+---------+------ x3o3o3o3o . ♦ 6 | 15 | 20 | 15 | 6 0 | 72 * x3o3o3o . *c3o ♦ 10 | 40 | 80 | 80 | 16 16 | * 27
oox3ooo3ooo3oxo *c3ooo&#xt → both heights = sqrt(3/8) = 0.612372 (pt || pseudo hin || tac) o..3o..3o..3o.. *c3o.. | 1 * * ♦ 16 0 0 0 | 80 0 0 0 0 | 160 0 0 0 0 0 0 | 80 40 0 0 0 0 0 0 0 0 | 10 16 0 0 0 0 .o.3.o.3.o.3.o. *c3.o. | * 16 * ♦ 1 10 5 0 | 10 30 10 30 0 | 30 20 10 10 30 60 0 | 20 10 5 5 10 30 20 20 0 0 | 5 5 10 1 5 0 ..o3..o3..o3..o *c3..o | * * 10 ♦ 0 0 8 8 | 0 0 32 24 24 | 0 0 0 48 48 32 32 | 0 0 0 32 24 32 8 8 8 8 | 1 0 8 8 8 1 ---------------------------+---------+-------------+-------------------+--------------------------+--------------------------------+----------------- oo.3oo.3oo.3oo. *c3oo.&#x | 1 1 0 | 16 * * * ♦ 10 0 0 0 0 | 30 0 0 0 0 0 0 | 20 10 0 0 0 0 0 0 0 0 | 5 5 0 0 0 0 ... ... ... .x. ... | 0 2 0 | * 80 * * ♦ 1 6 0 3 0 | 6 6 3 0 3 12 0 | 6 3 2 0 1 6 6 6 0 0 | 4 2 3 0 2 0 .oo3.oo3.oo3.oo *c3.oo&#x | 0 1 1 | * * 80 * ♦ 0 0 4 6 0 | 0 0 0 6 12 12 0 | 0 0 0 4 6 12 4 4 0 0 | 1 0 4 1 4 0 ..x ... ... ... ... | 0 0 2 | * * * 40 ♦ 0 0 4 0 6 | 0 0 0 12 6 0 12 | 0 0 0 12 6 4 0 0 4 4 | 0 0 1 4 4 1 ---------------------------+---------+-------------+-------------------+--------------------------+--------------------------------+----------------- ... ... ... ox. ...&#x | 1 2 0 | 2 1 0 0 | 80 * * * * ♦ 6 0 0 0 0 0 0 | 6 3 0 0 0 0 0 0 0 0 | 3 2 0 0 0 0 ... ... .o.3.x. ... | 0 3 0 | 0 3 0 0 | * 160 * * * ♦ 1 2 1 0 0 2 0 | 2 1 1 0 0 1 2 2 0 0 | 2 1 1 0 1 0 .ox ... ... ... ...&#x | 0 1 2 | 0 0 2 1 | * * 160 * * ♦ 0 0 0 3 3 0 0 | 0 0 0 3 3 3 0 0 0 0 | 0 0 1 1 3 0 ... ... ... .xo ...&#x | 0 2 1 | 0 1 2 0 | * * * 240 * ♦ 0 0 0 0 2 4 0 | 0 0 0 0 1 4 2 2 0 0 | 1 0 2 0 2 0 ..x3..o ... ... ... | 0 0 3 | 0 0 0 3 | * * * * 80 ♦ 0 0 0 2 0 0 4 | 0 0 0 4 1 0 0 0 2 2 | 0 0 0 2 2 1 ---------------------------+---------+-------------+-------------------+--------------------------+--------------------------------+----------------- ... ... oo.3ox. ...&#x ♦ 1 3 0 | 3 3 0 0 | 3 1 0 0 0 | 160 * * * * * * | 2 1 0 0 0 0 0 0 0 0 | 2 1 0 0 0 0 ... .o.3.o.3.x. ... ♦ 0 4 0 | 0 6 0 0 | 0 4 0 0 0 | * 80 * * * * * | 1 0 1 0 0 0 1 0 0 0 | 1 1 0 0 1 0 ... ... .o.3.x. *c3.o. ♦ 0 4 0 | 0 6 0 0 | 0 4 0 0 0 | * * 40 * * * * | 0 1 0 0 0 0 0 2 0 0 | 2 0 1 0 0 0 .ox3.oo ... ... ...&#x ♦ 0 1 3 | 0 0 3 3 | 0 0 3 0 1 | * * * 160 * * * | 0 0 0 2 1 0 0 0 0 0 | 0 0 0 1 2 0 .ox ... ... .xo ...&#x ♦ 0 2 2 | 0 1 4 1 | 0 0 2 2 0 | * * * * 240 * * | 0 0 0 0 1 2 0 0 0 0 | 0 0 1 0 2 0 ... ... .oo3.xo ...&#x ♦ 0 3 1 | 0 3 3 0 | 0 1 0 3 0 | * * * * * 320 * | 0 0 0 0 0 1 1 1 0 0 | 1 0 1 0 1 0 ..x3..o3..o ... ... ♦ 0 0 4 | 0 0 0 6 | 0 0 0 0 4 | * * * * * * 80 | 0 0 0 1 0 0 0 0 1 1 | 0 0 0 1 1 1 ---------------------------+---------+-------------+-------------------+--------------------------+--------------------------------+----------------- ... oo.3oo.3ox. ...&#x ♦ 1 4 0 | 4 6 0 0 | 6 4 0 0 0 | 4 1 0 0 0 0 0 | 80 * * * * * * * * * | 1 1 0 0 0 0 ... ... oo.3ox. *c3oo.&#x ♦ 1 4 0 | 4 6 0 0 | 6 4 0 0 0 | 4 0 1 0 0 0 0 | * 40 * * * * * * * * | 2 0 0 0 0 0 .o.3.o.3.o.3.x. ... ♦ 0 5 0 | 0 10 0 0 | 0 10 0 0 0 | 0 5 0 0 0 0 0 | * * 16 * * * * * * * | 0 1 0 0 1 0 .ox3.oo3.oo ... ...&#x ♦ 0 1 4 | 0 0 4 6 | 0 0 6 0 4 | 0 0 0 4 0 0 1 | * * * 80 * * * * * * | 0 0 0 1 1 0 .ox3.oo ... .xo ...&#x ♦ 0 2 3 | 0 1 6 3 | 0 0 6 3 1 | 0 0 0 2 3 0 0 | * * * * 80 * * * * * | 0 0 0 0 2 0 .ox ... .oo3.xo ...&#x ♦ 0 3 2 | 0 3 6 1 | 0 1 3 6 0 | 0 0 0 0 3 2 0 | * * * * * 160 * * * * | 0 0 1 0 1 0 ... .oo3.oo3.xo ...&#x ♦ 0 4 1 | 0 6 4 0 | 0 4 0 6 0 | 0 1 0 0 0 4 0 | * * * * * * 80 * * * | 1 0 0 0 1 0 ... ... .oo3.xo *c3.oo&#x ♦ 0 4 1 | 0 6 4 0 | 0 4 0 6 0 | 0 0 1 0 0 4 0 | * * * * * * * 80 * * | 1 0 1 0 0 0 ..x3..o3..o3..o ... ♦ 0 0 5 | 0 0 0 10 | 0 0 0 0 10 | 0 0 0 0 0 0 5 | * * * * * * * * 16 * | 0 0 0 0 1 1 ..x3..o3..o ... *c3..o ♦ 0 0 5 | 0 0 0 10 | 0 0 0 0 10 | 0 0 0 0 0 0 5 | * * * * * * * * * 16 | 0 0 0 1 0 1 ---------------------------+---------+-------------+-------------------+--------------------------+--------------------------------+----------------- ... ooo3ooo3oxo *c3ooo&#xt ♦ 1 8 1 | 8 24 8 0 | 24 32 0 24 0 | 32 8 8 0 0 32 0 | 8 8 0 0 0 0 8 8 0 0 | 10 * * * * * oo.3oo.3oo.3ox. ...&#x ♦ 1 5 0 | 5 10 0 0 | 10 10 0 0 0 | 10 5 0 0 0 0 0 | 5 0 1 0 0 0 0 0 0 0 | * 16 * * * * .ox ... .oo3.xo *c3.oo&#x ♦ 0 4 2 | 0 6 8 1 | 0 4 4 12 0 | 0 0 1 0 6 8 0 | 0 0 0 0 0 4 0 2 0 0 | * * 40 * * * .ox3.oo3.oo ... *c3.oo&#x ♦ 0 1 5 | 0 0 5 10 | 0 0 10 0 10 | 0 0 0 10 0 0 5 | 0 0 0 5 0 0 0 0 0 1 | * * * 16 * * .ox3.oo3.oo3.xo ...&#x ♦ 0 5 5 | 0 10 20 10 | 0 10 30 30 10 | 0 5 0 20 30 20 5 | 0 0 1 5 10 10 5 0 1 0 | * * * * 16 * ..x3..o3..o3..o *c3..o ♦ 0 0 10 | 0 0 0 40 | 0 0 0 0 80 | 0 0 0 0 0 0 80 | 0 0 0 0 0 0 0 0 16 16 | * * * * * 1
xox3ooo3ooo3oxo3ooo&#xt → both heights = 1/2 = 0.5 (hix || inv pseudo rix || hix) o..3o..3o..3o..3o.. & | 12 * ♦ 5 10 1 0 | 10 30 30 10 0 0 | 10 30 60 20 10 30 0 | 5 10 30 20 20 5 20 10 0 | 1 5 10 5 5 .o.3.o.3.o.3.o.3.o. | * 15 ♦ 0 8 0 8 | 0 12 48 4 12 4 | 0 8 48 48 24 24 8 | 0 2 16 24 24 16 24 12 2 | 0 4 8 6 8 --------------------------+-------+-------------+---------------------+---------------------------+-------------------------------+-------------- x.. ... ... ... ... & | 2 0 | 30 * * * ♦ 4 6 0 0 0 0 | 6 12 12 0 0 0 0 | 4 6 12 4 4 0 0 0 0 | 1 4 4 1 0 oo.3oo.3oo.3oo.3oo.&#x & | 1 1 | * 120 * * ♦ 0 3 6 1 0 0 | 0 3 12 6 3 6 0 | 0 1 6 6 6 2 6 3 0 | 0 2 3 3 2 o.o3o.o3o.o3o.o3o.o&#x | 2 0 | * * 6 * ♦ 0 0 0 10 0 0 | 0 0 0 0 0 30 0 | 0 0 0 0 0 0 20 10 0 | 0 0 0 5 5 ... ... ... .x. ... | 0 2 | * * * 60 ♦ 0 0 6 0 3 1 | 0 0 6 12 6 3 3 | 0 0 2 6 6 6 6 3 1 | 0 2 2 3 3 --------------------------+-------+-------------+---------------------+---------------------------+-------------------------------+-------------- x..3o.. ... ... ... & | 3 0 | 3 0 0 0 | 40 * * * * * ♦ 3 3 0 0 0 0 0 | 3 3 3 0 0 0 0 0 0 | 1 3 1 0 0 xo. ... ... ... ...&#x & | 2 1 | 1 2 0 0 | * 180 * * * * ♦ 0 2 4 0 0 0 0 | 0 1 4 2 2 0 0 0 0 | 0 2 2 1 0 ... ... ... ox. ...&#x & | 1 2 | 0 2 0 1 | * * 360 * * * ♦ 0 0 2 2 1 1 0 | 0 0 1 2 2 1 2 1 0 | 0 1 1 2 1 ooo3ooo3ooo3ooo3ooo&#xt | 2 1 | 0 2 1 0 | * * * 60 * * ♦ 0 0 0 0 0 6 0 | 0 0 0 0 0 0 6 3 0 | 0 0 0 3 2 ... ... .o.3.x. ... | 0 3 | 0 0 0 3 | * * * * 60 * ♦ 0 0 0 4 0 0 2 | 0 0 0 2 0 4 2 0 1 | 0 2 0 1 2 ... ... ... .x.3.o. | 0 3 | 0 0 0 3 | * * * * * 20 ♦ 0 0 0 0 6 0 0 | 0 0 0 0 6 0 0 3 0 | 0 0 2 3 0 --------------------------+-------+-------------+---------------------+---------------------------+-------------------------------+-------------- x..3o..3o.. ... ... & ♦ 4 0 | 6 0 0 0 | 4 0 0 0 0 0 | 30 * * * * * * | 2 1 0 0 0 0 0 0 0 | 1 2 0 0 0 xo.3oo. ... ... ...&#x & ♦ 3 1 | 3 3 0 0 | 1 3 0 0 0 0 | * 120 * * * * * | 0 1 2 0 0 0 0 0 0 | 0 2 1 0 0 xo. ... ... ox. ...&#x & ♦ 2 2 | 1 4 0 1 | 0 2 2 0 0 0 | * * 360 * * * * | 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0 ... ... oo.3ox. ...&#x & ♦ 1 3 | 0 3 0 3 | 0 0 3 0 1 0 | * * * 240 * * * | 0 0 0 1 0 1 1 0 0 | 0 1 0 1 1 ... ... ... ox.3oo.&#x & ♦ 1 3 | 0 3 0 3 | 0 0 3 0 0 1 | * * * * 120 * * | 0 0 0 0 2 0 0 1 0 | 0 0 1 2 0 ... ... ... oxo ...&#x ♦ 2 2 | 0 4 1 1 | 0 0 2 2 0 0 | * * * * * 180 * | 0 0 0 0 0 0 2 1 0 | 0 0 0 2 1 ... .o.3.o.3.x. ... ♦ 0 4 | 0 0 0 6 | 0 0 0 0 4 0 | * * * * * * 30 | 0 0 0 0 0 2 0 0 1 | 0 2 0 0 1 --------------------------+-------+-------------+---------------------+---------------------------+-------------------------------+-------------- x..3o..3o..3o.. ... & ♦ 5 0 | 10 0 0 0 | 10 0 0 0 0 0 | 5 0 0 0 0 0 0 | 12 * * * * * * * * | 1 1 0 0 0 xo.3oo.3oo. ... ...&#x & ♦ 4 1 | 6 4 0 0 | 4 6 0 0 0 0 | 1 4 0 0 0 0 0 | * 30 * * * * * * * | 0 2 0 0 0 xo.3oo. ... ox. ...&#x & ♦ 3 2 | 3 6 0 1 | 1 6 3 0 0 0 | 0 2 3 0 0 0 0 | * * 120 * * * * * * | 0 1 1 0 0 xo. ... oo.3ox. ...&#x & ♦ 2 3 | 1 6 0 3 | 0 3 6 0 1 0 | 0 0 3 2 0 0 0 | * * * 120 * * * * * | 0 1 0 1 0 xo. ... ... ox.3oo.&#x & ♦ 2 3 | 1 6 0 3 | 0 3 6 0 0 1 | 0 0 3 0 2 0 0 | * * * * 120 * * * * | 0 0 1 1 0 ... oo.3oo.3ox. ...&#x & ♦ 1 4 | 0 4 0 6 | 0 0 6 0 4 0 | 0 0 0 4 0 0 1 | * * * * * 60 * * * | 0 1 0 0 1 ... ... ooo3oxo ...&#x ♦ 2 3 | 0 6 1 3 | 0 0 6 3 1 0 | 0 0 0 2 0 3 0 | * * * * * * 120 * * | 0 0 0 1 1 ... ... ... oxo3ooo&#x ♦ 2 3 | 0 6 1 3 | 0 0 6 3 0 1 | 0 0 0 0 2 3 0 | * * * * * * * 60 * | 0 0 0 2 0 .o.3.o.3.o.3.x. ... ♦ 0 5 | 0 0 0 10 | 0 0 0 0 10 0 | 0 0 0 0 0 0 5 | * * * * * * * * 6 | 0 2 0 0 0 --------------------------+-------+-------------+---------------------+---------------------------+-------------------------------+-------------- x..3o..3o..3o..3o.. & ♦ 6 0 | 15 0 0 0 | 20 0 0 0 0 0 | 15 0 0 0 0 0 0 | 6 0 0 0 0 0 0 0 0 | 2 * * * * xo.3oo.3oo.3ox. ...&#x & ♦ 5 5 | 10 20 0 10 | 10 30 30 0 10 0 | 5 20 30 20 0 0 5 | 1 5 10 10 0 5 0 0 1 | * 12 * * * xo.3oo. ... ox.3oo.&#x & ♦ 3 3 | 3 9 0 3 | 1 9 9 0 0 1 | 0 3 9 0 3 0 0 | 0 0 3 0 3 0 0 0 0 | * * 40 * * xox ... ooo3oxo3ooo&#xt ♦ 4 6 | 2 24 2 12 | 0 12 48 12 4 4 | 0 0 24 16 16 24 0 | 0 0 0 8 8 0 8 8 0 | * * * 15 * ... ooo3ooo3oxo ...&#x ♦ 2 4 | 0 8 1 6 | 0 0 12 4 4 0 | 0 0 0 8 0 6 1 | 0 0 0 0 0 2 4 0 0 | * * * * 30
xoxo ooox3oxoo3oooo3ooxo&#xt all heights = sqrt(3/20) = 0.387298 (line || ortho pseudo rap || para inv pseudo penp || ortho pen) o... o...3o...3o...3o... | 2 * * * ♦ 1 10 5 0 0 0 0 0 0 0 | 10 30 10 30 0 0 0 0 0 0 0 0 0 0 0 0 0 | 30 10 20 10 60 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10 20 5 5 20 20 30 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 5 1 5 10 5 0 0 0 0 0 .o.. .o..3.o..3.o..3.o.. | * 10 * * ♦ 0 2 0 6 6 2 0 0 0 0 | 1 12 0 6 3 6 3 24 6 1 6 12 0 0 0 0 0 | 6 6 12 0 24 6 2 12 12 12 12 2 6 6 6 24 12 0 0 0 0 0 0 | 3 6 4 0 12 12 12 2 6 6 6 2 3 12 6 12 12 4 0 0 0 0 0 0 0 | 2 0 3 6 4 3 6 2 0 0 ..o. ..o.3..o.3..o.3..o. | * * 10 * ♦ 0 0 1 0 6 0 1 4 4 0 | 0 0 4 6 0 0 6 12 12 0 0 12 6 4 6 12 0 | 0 0 0 6 12 12 0 12 4 4 12 6 0 12 6 12 24 4 6 4 12 12 0 | 0 0 0 4 4 4 12 6 4 4 4 0 6 12 12 4 12 12 1 4 1 4 6 4 0 | 0 1 1 4 4 4 4 6 1 1 ...o ...o3...o3...o3...o | * * * 5 ♦ 0 0 0 0 0 4 0 0 8 4 | 0 0 0 0 0 0 0 0 0 4 6 24 0 4 24 12 6 | 0 0 0 0 0 0 0 0 0 0 0 0 4 12 24 24 24 0 12 24 24 8 4 | 0 0 0 0 0 0 0 0 0 0 0 1 12 12 24 8 12 8 0 12 8 12 8 2 1 | 0 0 0 0 2 6 4 8 4 2 -----------------------------+-----------+-----------------------------+------------------------------------------------------+-----------------------------------------------------------------------+-------------------------------------------------------------------------+------------------------- x... .... .... .... .... | 2 0 0 0 | 1 * * * * * * * * * ♦ 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 5 0 5 0 0 0 0 0 0 0 oo.. oo..3oo..3oo..3oo..&#x | 1 1 0 0 | * 20 * * * * * * * * ♦ 1 6 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 | 6 3 6 0 12 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3 6 2 0 6 6 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 0 3 3 2 0 0 0 0 0 o.o. o.o.3o.o.3o.o.3o.o.&#x | 1 0 1 0 | * * 10 * * * * * * * ♦ 0 0 4 6 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 6 12 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 4 4 4 12 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 1 4 4 0 0 0 0 0 .... .... .x.. .... .... | 0 2 0 0 | * * * 30 * * * * * * ♦ 0 2 0 0 1 2 0 4 0 0 1 0 0 0 0 0 0 | 1 2 4 0 4 0 1 2 4 4 2 0 2 0 0 4 0 0 0 0 0 0 0 | 1 2 2 0 4 4 2 0 2 2 2 1 0 2 0 4 2 0 0 0 0 0 0 0 0 | 1 0 2 2 2 1 2 0 0 0 .oo. .oo.3.oo.3.oo.3.oo.&#x | 0 1 1 0 | * * * * 60 * * * * * ♦ 0 0 0 1 0 0 1 4 2 0 0 2 0 0 0 0 0 | 0 0 0 0 4 2 0 4 2 2 4 1 0 2 1 4 4 0 0 0 0 0 0 | 0 0 0 0 2 2 4 1 2 2 2 0 1 4 2 2 4 2 0 0 0 0 0 0 0 | 0 0 1 2 2 2 2 1 0 0 .o.o .o.o3.o.o3.o.o3.o.o&#x | 0 1 0 1 | * * * * * 20 * * * * ♦ 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 0 3 3 6 12 6 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 1 3 6 6 6 6 2 0 0 0 0 0 0 0 | 0 0 0 0 2 3 3 2 0 0 ..x. .... .... .... .... | 0 0 2 0 | * * * * * * 5 * * * ♦ 0 0 0 0 0 0 6 0 0 0 0 0 0 4 0 0 0 | 0 0 0 0 0 0 0 12 0 0 0 0 0 12 0 0 0 0 6 0 0 0 0 | 0 0 0 0 0 0 0 0 4 4 0 0 6 12 0 0 0 0 0 4 0 0 0 0 0 | 0 0 1 0 0 4 4 0 1 0 .... .... .... .... ..x. | 0 0 2 0 | * * * * * * * 20 * * ♦ 0 0 1 0 0 0 0 0 3 0 0 0 3 0 0 3 0 | 0 0 0 3 0 3 0 0 0 0 3 3 0 0 0 0 6 3 0 0 3 6 0 | 0 0 0 3 0 0 3 3 0 0 1 0 0 0 3 0 3 6 1 0 0 1 3 3 0 | 0 1 0 1 3 1 0 3 0 1 ..oo ..oo3..oo3..oo3..oo&#x | 0 0 1 1 | * * * * * * * * 40 * ♦ 0 0 0 0 0 0 0 0 0 0 0 3 0 1 3 3 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 6 0 3 3 6 3 0 | 0 0 0 0 0 0 0 0 0 0 0 0 3 3 6 1 3 3 0 3 1 3 3 1 0 | 0 0 0 0 1 3 1 3 1 1 .... ...x .... .... .... | 0 0 0 2 | * * * * * * * * * 10 ♦ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 6 0 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 3 12 6 0 3 | 0 0 0 0 0 0 0 0 0 0 0 0 3 0 6 0 0 0 0 6 6 6 2 0 1 | 0 0 0 0 0 3 0 2 3 2 -----------------------------+-----------+-----------------------------+------------------------------------------------------+-----------------------------------------------------------------------+-------------------------------------------------------------------------+------------------------- xo.. .... .... .... ....&#x | 2 1 0 0 | 1 2 0 0 0 0 0 0 0 0 | 10 * * * * * * * * * * * * * * * * ♦ 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 0 3 0 0 0 0 0 0 0 .... .... ox.. .... ....&#x | 1 2 0 0 | 0 2 0 1 0 0 0 0 0 0 | * 60 * * * * * * * * * * * * * * * ♦ 1 1 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 1 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 0 2 1 1 0 0 0 0 0 .... .... .... .... o.x.&#x | 1 0 2 0 | 0 0 2 0 0 0 0 1 0 0 | * * 20 * * * * * * * * * * * * * * ♦ 0 0 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 3 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 1 3 0 0 0 0 0 ooo. ooo.3ooo.3ooo.3ooo.&#x | 1 1 1 0 | 0 1 1 0 1 0 0 0 0 0 | * * * 60 * * * * * * * * * * * * * ♦ 0 0 0 0 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 2 2 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 2 2 0 0 0 0 0 .... .o..3.x.. .... .... | 0 3 0 0 | 0 0 0 3 0 0 0 0 0 0 | * * * * 10 * * * * * * * * * * * * ♦ 0 2 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 0 0 0 4 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 2 2 0 1 0 0 0 0 .... .... .x..3.o.. .... | 0 3 0 0 | 0 0 0 3 0 0 0 0 0 0 | * * * * * 20 * * * * * * * * * * * ♦ 0 0 2 0 0 0 1 0 0 2 0 0 1 0 0 0 0 0 0 0 0 0 0 | 0 1 2 0 0 2 0 0 0 1 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 | 1 0 1 0 2 0 1 0 0 0 .ox. .... .... .... ....&#x | 0 1 2 0 | 0 0 0 0 2 0 1 0 0 0 | * * * * * * 30 * * * * * * * * * * ♦ 0 0 0 0 0 0 0 4 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 2 2 0 0 1 4 0 0 0 0 0 0 0 0 0 0 0 | 0 0 1 0 0 2 2 0 0 0 .... .... .xo. .... ....&#x | 0 2 1 0 | 0 0 0 1 2 0 0 0 0 0 | * * * * * * * 120 * * * * * * * * * ♦ 0 0 0 0 1 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 | 0 0 0 0 1 1 1 0 1 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 | 0 0 1 1 1 1 1 0 0 0 .... .... .... .... .ox.&#x | 0 1 2 0 | 0 0 0 0 2 0 0 1 0 0 | * * * * * * * * 60 * * * * * * * * ♦ 0 0 0 0 0 1 0 0 0 0 2 1 0 0 0 0 2 0 0 0 0 0 0 | 0 0 0 0 0 0 2 1 0 0 1 0 0 0 1 0 2 2 0 0 0 0 0 0 0 | 0 0 0 1 2 1 0 1 0 0 .... .o.x .... .... ....&#x | 0 1 0 2 | 0 0 0 0 0 2 0 0 0 1 | * * * * * * * * * 10 * * * * * * * ♦ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 3 0 6 0 0 0 0 0 0 0 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0 3 2 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 2 0 0 0 0 1 0 0 | * * * * * * * 20 * * ..xo ..ox3..oo3..oo ....&#x ♦ 0 0 2 4 | 0 0 0 0 0 0 1 0 8 6 | 0 0 0 0 0 0 0 0 0 0 0 0 0 4 12 0 4 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 8 0 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2 0 0 0 0 | * * * * * * * * 5 * .... ..ox3..oo3..oo3..xo&#x ♦ 0 0 5 5 | 0 0 0 0 0 0 0 10 20 10 | 0 0 0 0 0 0 0 0 0 0 0 0 10 0 30 30 10 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 20 30 20 5 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 5 10 10 5 1 | * * * * * * * * * 2
oxoxo xooxo3ooxoo oxoox3ooxoo&#xt → heights = 1/sqrt(12) = 0.288675 ({3} || perp trip || bidual triddip || para trip || perp {3}) ...
xo3oo3oo3ox3oo xo&#zx → height = 0 (tegum sum of hixip and inv. rix) o.3o.3o.3o.3o. o. | 12 * ♦ 5 1 10 0 | 10 30 30 10 0 0 | 10 30 60 20 10 30 0 | 5 10 30 20 20 5 20 10 0 | 1 5 10 5 5 .o3.o3.o3.o3.o .o | * 15 ♦ 0 0 8 8 | 0 12 48 4 12 4 | 0 8 48 48 24 24 8 | 0 2 16 24 24 16 24 12 2 | 0 4 8 6 8 ----------------------+-------+-------------+---------------------+---------------------------+-------------------------------+-------------- x. .. .. .. .. .. | 2 0 | 30 * * * ♦ 4 6 0 0 0 0 | 6 12 12 0 0 0 0 | 4 6 12 4 4 0 0 0 0 | 1 4 4 1 0 .. .. .. .. .. x. | 2 0 | * 6 * * ♦ 0 0 0 10 0 0 | 0 0 0 0 0 30 0 | 0 0 0 0 0 0 20 10 0 | 0 0 0 5 5 oo3oo3oo3oo3oo oo&#x | 1 1 | * * 120 * ♦ 0 3 6 1 0 0 | 0 3 12 6 3 6 0 | 0 1 6 6 6 2 6 3 0 | 0 2 3 3 2 .. .. .. .x .. .. | 0 2 | * * * 60 ♦ 0 0 6 0 3 1 | 0 0 6 12 6 3 3 | 0 0 2 6 6 6 6 3 1 | 0 2 2 3 3 ----------------------+-------+-------------+---------------------+---------------------------+-------------------------------+-------------- x.3o. .. .. .. .. | 3 0 | 3 0 0 0 | 40 * * * * * ♦ 3 3 0 0 0 0 0 | 3 3 3 0 0 0 0 0 0 | 1 3 1 0 0 xo .. .. .. .. ..&#x | 2 1 | 1 0 2 0 | * 180 * * * * ♦ 0 2 4 0 0 0 0 | 0 1 4 2 2 0 0 0 0 | 0 2 2 1 0 .. .. .. ox .. ..&#x | 1 2 | 0 0 2 1 | * * 360 * * * ♦ 0 0 2 2 1 1 0 | 0 0 1 2 2 1 2 1 0 | 0 1 1 2 1 .. .. .. .. .. xo&#x | 2 1 | 0 1 2 0 | * * * 60 * * ♦ 0 0 0 0 0 6 0 | 0 0 0 0 0 0 6 3 0 | 0 0 0 3 2 .. .. .o3.x .. .. | 0 3 | 0 0 0 3 | * * * * 60 * ♦ 0 0 0 4 0 0 2 | 0 0 0 2 0 4 2 0 1 | 0 2 0 1 2 .. .. .. .x3.o .. | 0 3 | 0 0 0 3 | * * * * * 20 ♦ 0 0 0 0 6 0 0 | 0 0 0 0 6 0 0 3 0 | 0 0 2 3 0 ----------------------+-------+-------------+---------------------+---------------------------+-------------------------------+-------------- x.3o.3o. .. .. .. ♦ 4 0 | 6 0 0 0 | 4 0 0 0 0 0 | 30 * * * * * * | 2 1 0 0 0 0 0 0 0 | 1 2 0 0 0 xo3oo .. .. .. ..&#x ♦ 3 1 | 3 0 3 0 | 1 3 0 0 0 0 | * 120 * * * * * | 0 1 2 0 0 0 0 0 0 | 0 2 1 0 0 xo .. .. ox .. ..&#x ♦ 2 2 | 1 0 4 1 | 0 2 2 0 0 0 | * * 360 * * * * | 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0 .. .. oo3ox .. ..&#x ♦ 1 3 | 0 0 3 3 | 0 0 3 0 1 0 | * * * 240 * * * | 0 0 0 1 0 1 1 0 0 | 0 1 0 1 1 .. .. .. ox3oo ..&#x ♦ 1 3 | 0 0 3 3 | 0 0 3 0 0 1 | * * * * 120 * * | 0 0 0 0 2 0 0 1 0 | 0 0 1 2 0 .. .. .. ox .. xo&#x ♦ 2 2 | 0 1 4 1 | 0 0 2 2 0 0 | * * * * * 180 * | 0 0 0 0 0 0 2 1 0 | 0 0 0 2 1 .. .o3.o3.x .. .. ♦ 0 4 | 0 0 0 6 | 0 0 0 0 4 0 | * * * * * * 30 | 0 0 0 0 0 2 0 0 1 | 0 2 0 0 1 ----------------------+-------+-------------+---------------------+---------------------------+-------------------------------+-------------- x.3o.3o.3o. .. .. ♦ 5 0 | 10 0 0 0 | 10 0 0 0 0 0 | 5 0 0 0 0 0 0 | 12 * * * * * * * * | 1 1 0 0 0 xo3oo3oo .. .. ..&#x ♦ 4 1 | 6 0 4 0 | 4 6 0 0 0 0 | 1 4 0 0 0 0 0 | * 30 * * * * * * * | 0 2 0 0 0 xo3oo .. ox .. ..&#x ♦ 3 2 | 3 0 6 1 | 1 6 3 0 0 0 | 0 2 3 0 0 0 0 | * * 120 * * * * * * | 0 1 1 0 0 xo .. oo3ox .. ..&#x ♦ 2 3 | 1 0 6 3 | 0 3 6 0 1 0 | 0 0 3 2 0 0 0 | * * * 120 * * * * * | 0 1 0 1 0 xo .. .. ox3oo ..&#x ♦ 2 3 | 1 0 6 3 | 0 3 6 0 0 1 | 0 0 3 0 2 0 0 | * * * * 120 * * * * | 0 0 1 1 0 .. oo3oo3ox .. ..&#x ♦ 1 4 | 0 0 4 6 | 0 0 6 0 4 0 | 0 0 0 4 0 0 1 | * * * * * 60 * * * | 0 1 0 0 1 .. .. oo3ox .. xo&#x ♦ 2 3 | 0 1 6 3 | 0 0 6 3 1 0 | 0 0 0 2 0 3 0 | * * * * * * 120 * * | 0 0 0 1 1 .. .. .. ox3oo xo&#x ♦ 2 3 | 0 1 6 3 | 0 0 6 3 0 1 | 0 0 0 0 2 3 0 | * * * * * * * 60 * | 0 0 0 2 0 .o3.o3.o3.x .. .. ♦ 0 5 | 0 0 0 10 | 0 0 0 0 10 0 | 0 0 0 0 0 0 5 | * * * * * * * * 6 | 0 2 0 0 0 ----------------------+-------+-------------+---------------------+---------------------------+-------------------------------+-------------- x.3o.3o.3o.3o. .. ♦ 6 0 | 15 0 0 0 | 20 0 0 0 0 0 | 15 0 0 0 0 0 0 | 6 0 0 0 0 0 0 0 0 | 2 * * * * xo3oo3oo3ox .. ..&#x ♦ 5 5 | 10 0 20 10 | 10 30 30 0 10 0 | 5 20 30 20 0 0 5 | 1 5 10 10 0 5 0 0 1 | * 12 * * * xo3oo .. ox3oo ..&#x ♦ 3 3 | 3 0 9 3 | 1 9 9 0 0 1 | 0 3 9 0 3 0 0 | 0 0 3 0 3 0 0 0 0 | * * 40 * * xo .. oo3ox3oo xo&#zx ♦ 4 6 | 2 2 24 12 | 0 12 48 12 4 4 | 0 0 24 16 16 24 0 | 0 0 0 8 8 0 8 8 0 | * * * 15 * .. oo3oo3ox .. xo&#x ♦ 2 4 | 0 1 8 6 | 0 0 12 4 4 0 | 0 0 0 8 0 6 1 | 0 0 0 0 0 2 4 0 0 | * * * * 30
xoo3oxo oxo3oox oox3xoo&#zx → all heights = 0 (tegum sum of 3 mutually gyro-orthogonal triddips) o..3o.. o..3o.. o..3o.. | 9 * * ♦ 2 2 6 6 0 0 0 0 0 | 1 1 6 3 6 12 12 6 3 6 24 0 0 0 0 0 0 0 0 | 6 6 2 12 6 6 12 6 2 6 24 12 12 12 12 24 0 0 0 0 0 | 2 3 4 6 6 3 4 2 12 12 12 6 6 12 6 12 12 0 0 0 0 | 2 2 3 4 6 3 6 0 .o.3.o. .o.3.o. .o.3.o. | * 9 * ♦ 0 0 6 0 2 2 6 0 0 | 0 0 3 6 12 6 0 0 0 0 24 1 1 12 6 3 6 0 0 | 6 6 6 12 2 0 0 0 0 0 12 24 24 12 12 12 6 6 12 6 2 | 3 2 6 4 0 0 0 0 12 6 6 12 12 12 12 12 6 3 6 4 2 | 2 0 3 3 6 4 6 2 ..o3..o ..o3..o ..o3..o | * * 9 ♦ 0 0 0 6 0 0 6 2 2 | 0 0 0 0 0 0 6 12 6 3 24 0 0 6 3 6 12 1 1 | 0 0 0 0 0 2 12 6 6 6 12 12 12 24 24 12 2 6 12 6 6 | 0 0 0 0 4 2 6 3 6 12 12 12 12 6 12 6 12 2 4 6 3 | 0 2 4 3 6 3 6 2 ----------------------------+-------+----------------------+-----------------------------------------------------+----------------------------------------------------------------------+----------------------------------------------------------+------------------ x.. ... ... ... ... ... | 2 0 0 | 9 * * * * * * * * ♦ 1 0 3 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 | 3 0 0 0 0 6 6 3 0 0 12 0 0 0 0 0 0 0 0 0 0 | 1 0 0 0 6 3 2 0 6 6 6 0 0 0 0 0 0 0 0 0 0 | 0 2 3 2 3 0 0 0 ... ... ... ... ... x.. | 2 0 0 | * 9 * * * * * * * ♦ 0 1 0 0 0 6 0 0 0 3 0 0 0 0 0 0 0 0 0 | 0 3 0 6 6 0 0 0 0 3 0 0 0 0 0 12 0 0 0 0 0 | 0 3 2 6 0 0 0 1 0 0 0 0 0 6 0 6 6 0 0 0 0 | 2 0 0 2 0 3 3 0 oo.3oo. oo.3oo. oo.3oo.&#x | 1 1 0 | * * 54 * * * * * * ♦ 0 0 1 1 2 2 0 0 0 0 4 0 0 0 0 0 0 0 0 | 2 2 1 4 1 0 0 0 0 0 4 4 4 2 2 4 0 0 0 0 0 | 1 1 2 2 0 0 0 0 4 2 2 2 2 4 2 4 2 0 0 0 0 | 1 0 1 2 2 2 2 0 o.o3o.o o.o3o.o o.o3o.o&#x | 1 0 1 | * * * 54 * * * * * ♦ 0 0 0 0 0 0 2 2 1 1 4 0 0 0 0 0 0 0 0 | 0 0 0 0 0 1 4 2 1 2 4 2 2 4 4 4 0 0 0 0 0 | 0 0 0 0 2 1 2 1 2 4 4 2 2 2 2 2 4 0 0 0 0 | 0 1 2 2 2 1 2 0 ... .x. ... ... ... ... | 0 2 0 | * * * * 9 * * * * ♦ 0 0 0 3 0 0 0 0 0 0 0 1 0 6 0 0 0 0 0 | 0 3 0 0 0 0 0 0 0 0 0 12 0 0 0 0 6 3 6 0 0 | 0 1 0 0 0 0 0 0 0 0 0 6 6 6 0 0 0 3 6 2 0 | 0 0 3 0 0 2 3 2 ... ... .x. ... ... ... | 0 2 0 | * * * * * 9 * * * ♦ 0 0 0 0 6 0 0 0 0 0 0 0 1 0 3 0 0 0 0 | 3 0 6 6 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 3 0 | 3 0 6 2 0 0 0 0 6 0 0 0 0 0 6 6 0 0 0 0 1 | 2 0 0 3 3 2 0 0 .oo3.oo .oo3.oo .oo3.oo&#x | 0 1 1 | * * * * * * 54 * * ♦ 0 0 0 0 0 0 0 0 0 0 4 0 0 2 1 1 2 0 0 | 0 0 0 0 0 0 0 0 0 0 2 4 4 4 4 2 1 2 4 2 1 | 0 0 0 0 0 0 0 0 2 2 2 4 4 2 4 2 2 1 2 2 1 | 0 0 2 1 2 2 2 1 ... ... ... ..x ... ... | 0 0 2 | * * * * * * * 9 * ♦ 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 3 0 1 0 | 0 0 0 0 0 0 6 0 6 3 0 0 0 12 0 0 0 3 0 0 0 | 0 0 0 0 2 0 2 1 0 6 0 6 0 0 0 0 6 1 0 0 0 | 0 2 2 3 0 0 3 0 ... ... ... ... ..x ... | 0 0 2 | * * * * * * * * 9 ♦ 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 6 0 1 | 0 0 0 0 0 0 0 3 0 0 0 0 0 0 12 0 0 0 6 3 6 | 0 0 0 0 0 1 0 0 0 0 6 0 6 0 6 0 0 0 2 6 3 | 0 0 2 0 3 3 0 2 ----------------------------+-------+----------------------+-----------------------------------------------------+----------------------------------------------------------------------+----------------------------------------------------------+------------------ x..3o.. ... ... ... ... | 3 0 0 | 3 0 0 0 0 0 0 0 0 | 3 * * * * * * * * * * * * * * * * * * ♦ 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 6 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 2 3 0 0 0 0 0 ... ... ... ... o..3x.. | 3 0 0 | 0 3 0 0 0 0 0 0 0 | * 3 * * * * * * * * * * * * * * * * * ♦ 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 3 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 0 0 0 0 3 0 0 xo. ... ... ... ... ...&#x | 2 1 0 | 1 0 2 0 0 0 0 0 0 | * * 27 * * * * * * * * * * * * * * * * ♦ 2 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 | 1 0 0 0 0 0 0 0 4 2 2 0 0 0 0 0 0 0 0 0 0 | 0 0 1 2 2 0 0 0 ... ox. ... ... ... ...&#x | 1 2 0 | 0 0 2 0 1 0 0 0 0 | * * * 27 * * * * * * * * * * * * * * * ♦ 0 2 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 | 0 1 0 0 0 0 0 0 0 0 0 2 2 4 0 0 0 0 0 0 0 | 0 0 1 0 0 2 2 0 ... ... ox. ... ... ...&#x | 1 2 0 | 0 0 2 0 0 1 0 0 0 | * * * * 54 * * * * * * * * * * * * * * ♦ 1 0 1 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 | 1 0 2 1 0 0 0 0 2 0 0 0 0 0 1 2 0 0 0 0 0 | 1 0 0 2 1 1 0 0 ... ... ... ... ... xo.&#x | 2 1 0 | 0 1 2 0 0 0 0 0 0 | * * * * * 54 * * * * * * * * * * * * * ♦ 0 1 0 2 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 | 0 1 1 2 0 0 0 0 0 0 0 0 0 2 0 2 1 0 0 0 0 | 1 0 0 1 0 2 1 0 x.o ... ... ... ... ...&#x | 2 0 1 | 1 0 0 2 0 0 0 0 0 | * * * * * * 54 * * * * * * * * * * * * ♦ 0 0 0 0 0 1 2 1 0 0 2 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 2 1 1 0 1 2 2 0 0 0 0 0 0 0 0 0 0 | 0 1 2 1 1 0 0 0 ... ... ... o.x ... ...&#x | 1 0 2 | 0 0 0 2 0 0 0 1 0 | * * * * * * * 54 * * * * * * * * * * * ♦ 0 0 0 0 0 0 2 0 1 1 0 0 0 2 0 0 0 0 0 0 0 | 0 0 0 0 1 0 2 1 0 2 0 1 0 0 0 0 2 0 0 0 0 | 0 1 1 2 0 0 1 0 ... ... ... ... o.x ...&#x | 1 0 2 | 0 0 0 2 0 0 0 0 1 | * * * * * * * * 27 * * * * * * * * * * ♦ 0 0 0 0 0 0 0 2 0 0 0 0 0 0 4 0 0 0 0 0 0 | 0 0 0 0 0 1 0 0 0 0 4 0 2 0 2 0 0 0 0 0 0 | 0 0 2 0 2 1 0 0 ... ... ... ... ... x.o&#x | 2 0 1 | 0 1 0 2 0 0 0 0 0 | * * * * * * * * * 27 * * * * * * * * * ♦ 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 4 0 0 0 0 0 | 0 0 0 0 0 0 0 1 0 0 0 0 0 2 0 2 4 0 0 0 0 | 0 0 0 2 0 1 2 0 ooo3ooo ooo3ooo ooo3ooo&#x | 1 1 1 | 0 0 1 1 0 0 1 0 0 | * * * * * * * * * * 216 * * * * * * * * ♦ 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 | 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 | 0 0 1 1 1 1 1 0 .o.3.x. ... ... ... ... | 0 3 0 | 0 0 0 0 3 0 0 0 0 | * * * * * * * * * * * 3 * * * * * * * ♦ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 6 0 0 | 0 0 3 0 0 0 0 2 ... ... .x.3.o. ... ... | 0 3 0 | 0 0 0 0 0 3 0 0 0 | * * * * * * * * * * * * 3 * * * * * * ♦ 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 3 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 2 0 0 3 0 0 0 0 ... .xo ... ... ... ...&#x | 0 2 1 | 0 0 0 0 1 0 2 0 0 | * * * * * * * * * * * * * 54 * * * * * ♦ 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 1 2 0 0 | 0 0 0 0 0 0 0 0 0 0 0 2 2 1 0 0 0 1 2 1 0 | 0 0 2 0 0 1 1 1 ... ... .xo ... ... ...&#x | 0 2 1 | 0 0 0 0 0 1 2 0 0 | * * * * * * * * * * * * * * 27 * * * * ♦ 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 0 | 0 0 0 0 0 0 0 0 2 0 0 0 0 0 4 2 0 0 0 0 1 | 0 0 0 1 2 2 0 0 ... ... ... .ox ... ...&#x | 0 1 2 | 0 0 0 0 0 0 2 1 0 | * * * * * * * * * * * * * * * 27 * * * ♦ 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 2 0 0 0 | 0 0 0 0 0 0 0 0 0 2 0 4 0 0 0 0 2 1 0 0 0 | 0 0 2 1 0 0 2 0 ... ... ... ... .ox ...&#x | 0 1 2 | 0 0 0 0 0 0 2 0 1 | * * * * * * * * * * * * * * * * 54 * * ♦ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 1 1 | 0 0 0 0 0 0 0 0 0 0 1 0 2 0 2 0 0 0 1 0 0 | 0 0 1 0 1 2 0 1 ... ... ..o3..x ... ... | 0 0 3 | 0 0 0 0 0 0 0 3 0 | * * * * * * * * * * * * * * * * * 3 * ♦ 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 6 3 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 2 0 3 0 0 0 0 ... ... ... ... ..x3..o | 0 0 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 0 0 0 0 0 0 6 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 3 | 0 0 0 0 0 3 0 2 ----------------------------+-------+----------------------+-----------------------------------------------------+----------------------------------------------------------------------+----------------------------------------------------------+------------------ xo. ... ox. ... ... ...&#x ♦ 2 2 0 | 1 0 4 0 0 1 0 0 0 | 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 27 * * * * * * * * * * * * * * * * * * * * | 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 2 1 0 0 0 ... ox. ... ... ... xo.&#x ♦ 2 2 0 | 0 1 4 0 1 0 0 0 0 | 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 27 * * * * * * * * * * * * * * * * * * * | 0 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 | 0 0 0 0 0 2 1 0 ... ... ox.3oo. ... ...&#x ♦ 1 3 0 | 0 0 3 0 0 3 0 0 0 | 0 0 0 0 3 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | * * 18 * * * * * * * * * * * * * * * * * * | 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 0 0 2 0 0 0 0 ... ... ox. ... ... xo.&#x ♦ 2 2 0 | 0 1 4 0 0 1 0 0 0 | 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * 54 * * * * * * * * * * * * * * * * * | 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | 1 0 0 1 0 1 0 0 ... ... ... ... oo.3xo.&#x ♦ 3 1 0 | 0 3 3 0 0 0 0 0 0 | 0 1 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * 18 * * * * * * * * * * * * * * * * | 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 0 0 0 0 2 0 0 x.o3o.o ... ... ... ...&#x ♦ 3 0 1 | 3 0 0 3 0 0 0 0 0 | 1 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * * 18 * * * * * * * * * * * * * * * | 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 2 0 0 0 0 0 x.o ... ... o.x ... ...&#x ♦ 2 0 2 | 1 0 0 4 0 0 0 1 0 | 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 | * * * * * * 54 * * * * * * * * * * * * * * | 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 0 x.o ... ... ... o.x ...&#x ♦ 2 0 2 | 1 0 0 4 0 0 0 0 1 | 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 | * * * * * * * 27 * * * * * * * * * * * * * | 0 0 0 0 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 | 0 0 2 0 1 0 0 0 ... ... o.o3o.x ... ...&#x ♦ 1 0 3 | 0 0 0 3 0 0 0 3 0 | 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 1 0 | * * * * * * * * 18 * * * * * * * * * * * * | 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 1 0 2 0 0 0 0 ... ... ... o.x ... x.o&#x ♦ 2 0 2 | 0 1 0 4 0 0 0 1 0 | 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 | * * * * * * * * * 27 * * * * * * * * * * * | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2 0 0 0 0 | 0 0 0 2 0 0 1 0 xoo ... ... ... ... ...&#x ♦ 2 1 1 | 1 0 2 2 0 0 1 0 0 | 0 0 1 0 0 0 1 0 0 0 2 0 0 0 0 0 0 0 0 | * * * * * * * * * * 108 * * * * * * * * * * | 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 | 0 0 1 1 1 0 0 0 ... oxo ... ... ... ...&#x ♦ 1 2 1 | 0 0 2 1 1 0 2 0 0 | 0 0 0 1 0 0 0 0 0 0 2 0 0 1 0 0 0 0 0 | * * * * * * * * * * * 108 * * * * * * * * * | 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 | 0 0 1 0 0 1 1 0 ... ... oxo ... ... ...&#x ♦ 1 2 1 | 0 0 2 1 0 1 2 0 0 | 0 0 0 0 1 0 0 0 0 0 2 0 0 0 1 0 0 0 0 | * * * * * * * * * * * * 108 * * * * * * * * | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 | 0 0 0 1 1 1 0 0 ... ... ... oox ... ...&#x ♦ 1 1 2 | 0 0 1 2 0 0 2 1 0 | 0 0 0 0 0 0 0 1 0 0 2 0 0 0 0 1 0 0 0 | * * * * * * * * * * * * * 108 * * * * * * * | 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 | 0 0 1 1 0 1 0 0 ... ... ... ... oox ...&#x ♦ 1 1 2 | 0 0 1 2 0 0 2 0 1 | 0 0 0 0 0 0 0 0 1 0 2 0 0 0 0 0 1 0 0 | * * * * * * * * * * * * * * 108 * * * * * * | 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 | 0 0 1 0 1 1 0 0 ... ... ... ... ... xoo&#x ♦ 2 1 1 | 0 1 2 2 0 0 1 0 0 | 0 0 0 0 0 1 0 0 0 1 2 0 0 0 0 0 0 0 0 | * * * * * * * * * * * * * * * 108 * * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 | 0 0 0 1 0 1 1 0 .oo3.xo ... ... ... ...&#x ♦ 0 3 1 | 0 0 0 0 3 0 3 0 0 | 0 0 0 0 0 0 0 0 0 0 0 1 0 3 0 0 0 0 0 | * * * * * * * * * * * * * * * * 18 * * * * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 | 0 0 2 0 0 0 0 1 ... .xo ... .ox ... ...&#x ♦ 0 2 2 | 0 0 0 0 1 0 4 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 | * * * * * * * * * * * * * * * * * 27 * * * | 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 1 0 0 0 | 0 0 2 0 0 0 1 0 ... .xo ... ... .ox ...&#x ♦ 0 2 2 | 0 0 0 0 1 0 4 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 | * * * * * * * * * * * * * * * * * * 54 * * | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 | 0 0 1 0 0 1 0 1 ... ... .xo ... .ox ...&#x ♦ 0 2 2 | 0 0 0 0 0 1 4 0 1 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 | * * * * * * * * * * * * * * * * * * * 27 * | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 1 | 0 0 0 0 1 2 0 0 ... ... ... ... .ox3.oo&#x ♦ 0 1 3 | 0 0 0 0 0 0 3 0 3 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 | * * * * * * * * * * * * * * * * * * * * 18 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 | 0 0 0 0 0 2 0 1 ----------------------------+-------+----------------------+-----------------------------------------------------+----------------------------------------------------------------------+----------------------------------------------------------+------------------ xo. ... ox.3oo. ... ...&#x ♦ 2 3 0 | 1 0 6 0 0 3 0 0 0 | 0 0 3 0 6 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | 3 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 9 * * * * * * * * * * * * * * * * * * * * | 0 0 0 2 0 0 0 0 ... ox. ... ... oo.3xo.&#x ♦ 3 2 0 | 0 3 6 0 1 0 0 0 0 | 0 1 0 3 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 3 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 9 * * * * * * * * * * * * * * * * * * * | 0 0 0 0 0 2 0 0 ... ... ox.3oo. ... xo.&#x ♦ 2 3 0 | 0 1 6 0 0 3 0 0 0 | 0 0 0 0 6 3 0 0 0 0 0 0 1 0 0 0 0 0 0 | 0 0 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * 18 * * * * * * * * * * * * * * * * * * | 1 0 0 1 0 0 0 0 ... ... ox. ... oo.3xo.&#x ♦ 3 2 0 | 0 3 6 0 0 1 0 0 0 | 0 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 | * * * 18 * * * * * * * * * * * * * * * * * | 1 0 0 0 0 1 0 0 x.o3o.o ... o.x ... ...&#x ♦ 3 0 2 | 3 0 0 6 0 0 0 1 0 | 1 0 0 0 0 0 6 3 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * * * * 18 * * * * * * * * * * * * * * * * | 0 1 1 0 0 0 0 0 x.o3o.o ... ... o.x ...&#x ♦ 3 0 2 | 3 0 0 6 0 0 0 0 1 | 1 0 0 0 0 0 6 0 3 0 0 0 0 0 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