Acronym | rez (old: rhio) | |||
Name |
rectified hecatonicosoctaexon, lattice B7 contact polytope (span of its small roots), lattice D7 contact polytope (span of its roots), equatorial cross-section of zee-first fy, equatorial cross-section of zee-first rek | |||
Cross sections |
© | |||
Circumradius | 1 | |||
Inradius wrt. gee | 1/sqrt(2) = 0.707107 | |||
Inradius wrt. ril | sqrt(2/7) = 0.534522 | |||
Lace city in approx. ASCII-art |
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h H -- x3o3o3o3o4o (gee) r S R -- o3x3o3o3o4o (rag) h H -- x3o3o3o3o4o (gee) \ \ \ \ \ +- o3x3o3o3o3o (ril) \ +---- x3o3o3o3o3x (staf) +------- o3o3o3o3x3o (inv. ril) where: h = x3o3o3o3o (hix) H = o3o3o3o3x (dual hix) r = o3x3o3o3o (rix) R = o3o3o3x3o (inv. rix) S = x3o3o3o3x (scad) | ||||
Lace hyper city in approx. ASCII-art |
where: o = o3o3o4o (point) H = x3o3o4o (hex) I = o3x3o4o (ico) | |||
Coordinates | (1/sqrt(2), 1/sqrt(2), 0, 0, 0, 0, 0) & all permutations, all changes of sign | |||
Volume | 121 sqrt(2)/630 = 0.271619 | |||
Surface | (7+57 sqrt(7))/45 = 3.506841 | |||
Dihedral angles | ||||
Face vector | 84, 840, 2520, 3920, 3360, 1344, 142 | |||
Confer |
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External links |
Incidence matrix according to Dynkin symbol
o3x3o3o3o3o4o . . . . . . . | 84 ♦ 20 | 10 80 | 40 160 | 80 160 | 80 64 | 32 2 --------------+----+-----+----------+----------+----------+---------+------- . x . . . . . | 2 | 840 | 1 8 | 8 24 | 24 32 | 32 16 | 16 1 --------------+----+-----+----------+----------+----------+---------+------- o3x . . . . . | 3 | 3 | 280 * ♦ 8 0 | 24 0 | 32 0 | 16 0 . x3o . . . . | 3 | 3 | * 2240 | 1 6 | 6 12 | 12 8 | 8 1 --------------+----+-----+----------+----------+----------+---------+------- o3x3o . . . . ♦ 6 | 12 | 4 4 | 560 * ♦ 6 0 | 12 0 | 8 0 . x3o3o . . . ♦ 4 | 6 | 0 4 | * 3360 | 1 4 | 4 4 | 4 1 --------------+----+-----+----------+----------+----------+---------+------- o3x3o3o . . . ♦ 10 | 30 | 10 20 | 5 5 | 672 * | 4 0 | 4 0 . x3o3o3o . . ♦ 5 | 10 | 0 10 | 0 5 | * 2688 | 1 2 | 2 1 --------------+----+-----+----------+----------+----------+---------+------- o3x3o3o3o . . ♦ 15 | 60 | 20 60 | 15 30 | 6 6 | 448 * | 2 0 . x3o3o3o3o . ♦ 6 | 15 | 0 20 | 0 15 | 0 6 | * 896 | 1 1 --------------+----+-----+----------+----------+----------+---------+------- o3x3o3o3o3o . ♦ 21 | 105 | 35 140 | 35 105 | 21 42 | 7 7 | 128 * . x3o3o3o3o4o ♦ 12 | 60 | 0 160 | 0 240 | 0 192 | 0 64 | * 14
o3x3o3o3o3o4/3o . . . . . . . | 84 ♦ 20 | 10 80 | 40 160 | 80 160 | 80 64 | 32 2 ----------------+----+-----+----------+----------+----------+---------+------- . x . . . . . | 2 | 840 | 1 8 | 8 24 | 24 32 | 32 16 | 16 1 ----------------+----+-----+----------+----------+----------+---------+------- o3x . . . . . | 3 | 3 | 280 * ♦ 8 0 | 24 0 | 32 0 | 16 0 . x3o . . . . | 3 | 3 | * 2240 | 1 6 | 6 12 | 12 8 | 8 1 ----------------+----+-----+----------+----------+----------+---------+------- o3x3o . . . . ♦ 6 | 12 | 4 4 | 560 * ♦ 6 0 | 12 0 | 8 0 . x3o3o . . . ♦ 4 | 6 | 0 4 | * 3360 | 1 4 | 4 4 | 4 1 ----------------+----+-----+----------+----------+----------+---------+------- o3x3o3o . . . ♦ 10 | 30 | 10 20 | 5 5 | 672 * | 4 0 | 4 0 . x3o3o3o . . ♦ 5 | 10 | 0 10 | 0 5 | * 2688 | 1 2 | 2 1 ----------------+----+-----+----------+----------+----------+---------+------- o3x3o3o3o . . ♦ 15 | 60 | 20 60 | 15 30 | 6 6 | 448 * | 2 0 . x3o3o3o3o . ♦ 6 | 15 | 0 20 | 0 15 | 0 6 | * 896 | 1 1 ----------------+----+-----+----------+----------+----------+---------+------- o3x3o3o3o3o . ♦ 21 | 105 | 35 140 | 35 105 | 21 42 | 7 7 | 128 * . x3o3o3o3o4/3o ♦ 12 | 60 | 0 160 | 0 240 | 0 192 | 0 64 | * 14
o3o3o *b3o3o3x3o . . . . . . . | 84 ♦ 20 | 80 10 | 160 40 | 160 80 | 32 32 80 | 2 16 16 -----------------+----+-----+----------+----------+----------+-------------+--------- . . . . . x . | 2 | 840 | 8 1 | 24 8 | 32 24 | 8 8 32 | 1 8 8 -----------------+----+-----+----------+----------+----------+-------------+--------- . . . . o3x . | 3 | 3 | 2240 * | 6 1 | 12 6 | 4 4 12 | 1 4 4 . . . . . x3o | 3 | 3 | * 280 ♦ 0 8 | 0 24 | 0 0 32 | 0 8 8 -----------------+----+-----+----------+----------+----------+-------------+--------- . . . o3o3x . ♦ 4 | 6 | 4 0 | 3360 * | 4 1 | 2 2 4 | 1 2 2 . . . . o3x3o ♦ 6 | 12 | 4 4 | * 560 ♦ 0 6 | 0 0 12 | 0 4 4 -----------------+----+-----+----------+----------+----------+-------------+--------- . o . *b3o3o3x . ♦ 5 | 10 | 10 0 | 5 0 | 2688 * | 1 1 1 | 1 1 1 . . . o3o3x3o ♦ 10 | 30 | 20 10 | 5 5 | * 672 | 0 0 4 | 0 2 2 -----------------+----+-----+----------+----------+----------+-------------+--------- o3o . *b3o3o3x . ♦ 6 | 15 | 20 0 | 15 0 | 6 0 | 448 * * | 1 1 0 . o3o *b3o3o3x . ♦ 6 | 15 | 20 0 | 15 0 | 6 0 | * 448 * | 1 0 1 . o . *b3o3o3x3o ♦ 15 | 60 | 60 20 | 30 15 | 6 6 | * * 448 | 0 1 1 -----------------+----+-----+----------+----------+----------+-------------+--------- o3o3o *b3o3o3x . ♦ 12 | 60 | 160 0 | 240 0 | 192 0 | 32 32 0 | 14 * * o3o . *b3o3o3x3o ♦ 21 | 105 | 140 35 | 105 35 | 42 21 | 7 0 7 | * 64 * . o3o *b3o3o3x3o ♦ 21 | 105 | 140 35 | 105 35 | 42 21 | 0 7 7 | * * 64
xox3oxo3ooo3ooo3ooo4ooo&#xt → both heights = 1/sqrt(2) = 0.707107 (gee || (pseudo) rag || gee) o..3o..3o..3o..3o..4o.. & | 24 * ♦ 10 10 0 | 40 10 40 0 0 | 80 40 80 0 0 | 80 80 80 0 0 | 32 80 32 0 | 1 32 1 .o.3.o.3.o.3.o.3.o.4.o. | * 60 ♦ 0 4 16 | 0 2 32 8 48 | 0 16 96 24 64 | 0 48 128 32 32 | 0 64 64 16 | 0 32 2 -----------------------------+-------+-------------+---------------------+----------------------+----------------------+----------------+--------- x.. ... ... ... ... ... & | 2 0 | 120 * * | 8 1 0 0 0 | 24 8 0 0 0 | 32 24 0 0 0 | 16 32 0 0 | 1 16 0 oo.3oo.3oo.3oo.3oo.4oo.&#x & | 1 1 | * 240 * | 0 1 8 0 0 | 0 8 24 0 0 | 0 24 32 0 0 | 0 32 16 0 | 0 16 1 ... .x. ... ... ... ... | 0 2 | * * 480 | 0 0 2 1 6 | 0 2 12 6 12 | 0 12 24 12 8 | 0 24 16 8 | 0 16 1 -----------------------------+-------+-------------+---------------------+----------------------+----------------------+----------------+--------- x..3o.. ... ... ... ... & | 3 0 | 3 0 0 | 320 * * * * | 6 1 0 0 0 | 12 6 0 0 0 | 8 12 0 0 | 1 8 0 xo. ... ... ... ... ...&#x & | 2 1 | 1 2 0 | * 120 * * * ♦ 0 8 0 0 0 | 0 24 0 0 0 | 0 32 0 0 | 0 16 0 ... ox. ... ... ... ...&#x & | 1 2 | 0 2 1 | * * 960 * * | 0 1 6 0 0 | 0 6 12 0 0 | 0 12 8 0 | 0 8 1 .o.3.x. ... ... ... ... | 0 3 | 0 0 3 | * * * 160 * ♦ 0 2 0 6 0 | 0 12 0 12 0 | 0 24 0 8 | 0 16 0 ... .x.3.o. ... ... ... | 0 3 | 0 0 3 | * * * * 960 | 0 0 2 1 4 | 0 2 8 4 4 | 0 8 8 4 | 0 8 1 -----------------------------+-------+-------------+---------------------+----------------------+----------------------+----------------+--------- x..3o..3o.. ... ... ... & ♦ 4 0 | 6 0 0 | 4 0 0 0 0 | 480 * * * * | 4 1 0 0 0 | 4 4 0 0 | 1 4 0 xo.3ox. ... ... ... ...&#x & ♦ 3 3 | 3 6 3 | 1 3 3 1 0 | * 320 * * * ♦ 0 6 0 0 0 | 0 12 0 0 | 0 8 0 ... ox.3oo. ... ... ...&#x & ♦ 1 3 | 0 3 3 | 0 0 3 0 1 | * * 1920 * * | 0 1 4 0 0 | 0 4 4 0 | 0 4 1 .o.3.x.3.o. ... ... ... ♦ 0 6 | 0 0 12 | 0 0 0 4 4 | * * * 240 * ♦ 0 2 0 4 0 | 0 8 0 4 | 0 8 0 ... .x.3.o.3.o. ... ... ♦ 0 4 | 0 0 6 | 0 0 0 0 4 | * * * * 960 | 0 0 2 1 2 | 0 2 4 2 | 0 4 1 -----------------------------+-------+-------------+---------------------+----------------------+----------------------+----------------+--------- x..3o..3o..3o.. ... ... & ♦ 5 0 | 10 0 0 | 10 0 0 0 0 | 5 0 0 0 0 | 384 * * * * | 2 1 0 0 | 1 2 0 xo.3ox.3oo. ... ... ...&#x & ♦ 4 6 | 6 12 12 | 4 6 12 4 4 | 1 4 4 1 0 | * 480 * * * | 0 4 0 0 | 0 4 0 ... ox.3oo.3oo. ... ...&#x & ♦ 1 4 | 0 4 6 | 0 0 6 0 4 | 0 0 4 0 1 | * * 1920 * * | 0 1 2 0 | 0 2 1 .o.3.x.3.o.3.o. ... ... ♦ 0 10 | 0 0 30 | 0 0 0 10 20 | 0 0 0 5 5 | * * * 192 * | 0 2 0 2 | 0 4 0 ... .x.3.o.3.o.3.o. ... ♦ 0 5 | 0 0 10 | 0 0 0 0 10 | 0 0 0 0 5 | * * * * 384 | 0 0 2 1 | 0 2 1 -----------------------------+-------+-------------+---------------------+----------------------+----------------------+----------------+--------- x..3o..3o..3o..3o.. ... & ♦ 6 0 | 15 0 0 | 20 0 0 0 0 | 15 0 0 0 0 | 6 0 0 0 0 | 128 * * * | 1 1 0 xo.3ox.3oo.3oo. ... ...&#x & ♦ 5 10 | 10 20 30 | 10 10 30 10 20 | 5 10 20 5 5 | 1 5 5 1 0 | * 384 * * | 0 2 0 ... ox.3oo.3oo.3oo. ...&#x & ♦ 1 5 | 0 5 10 | 0 0 10 0 10 | 0 0 10 0 5 | 0 0 5 0 1 | * * 768 * | 0 1 1 .o.3.x.3.o.3.o.3.o. ... ♦ 0 15 | 0 0 60 | 0 0 0 20 60 | 0 0 0 15 30 | 0 0 0 6 6 | * * * 64 | 0 2 0 -----------------------------+-------+-------------+---------------------+----------------------+----------------------+----------------+--------- x..3o..3o..3o..3o..4o.. & ♦ 12 0 | 60 0 0 | 160 0 0 0 0 | 240 0 0 0 0 | 192 0 0 0 0 | 64 0 0 0 | 2 * * xo.3ox.3oo.3oo.3oo. ...&#x & ♦ 6 15 | 15 30 60 | 20 15 60 20 60 | 15 20 60 15 30 | 6 15 30 6 6 | 1 6 6 1 | * 128 * ... oxo3ooo3ooo3ooo4ooo&#xt ♦ 2 10 | 0 20 40 | 0 0 80 0 80 | 0 0 160 0 80 | 0 0 160 0 32 | 0 0 64 0 | * * 12
oxo3xoo3ooo3ooo3oox3oxo&#xt → both heights = sqrt(2/7) = 0.534522 (ril || (pseudo) staf || inv ril) o..3o..3o..3o..3o..3o.. & | 42 * ♦ 10 10 0 | 5 20 5 40 20 0 | 10 20 20 10 60 60 20 0 | 10 10 30 40 40 60 40 10 0 | 5 2 20 35 20 10 20 20 10 2 0 | 1 5 11 15 2 .o.3.o.3.o.3.o.3.o.3.o. | * 42 ♦ 0 10 10 | 0 0 10 20 40 20 | 0 0 20 20 20 60 60 20 | 0 0 20 60 10 40 60 40 10 | 0 0 10 40 30 2 10 20 20 10 2 | 0 2 10 20 2 ------------------------------+-------+-------------+------------------------+---------------------------------+----------------------------------+---------------------------------------+-------------- ... x.. ... ... ... ... & | 2 0 | 210 * * | 1 4 0 4 0 0 | 4 6 4 0 12 6 0 0 | 6 4 12 6 12 12 4 0 0 | 4 1 12 12 4 4 6 4 1 0 0 | 1 4 6 5 1 oo.3oo.3oo.3oo.3oo.3oo.&#x & | 1 1 | * 420 * | 0 0 1 4 4 0 | 0 0 4 4 6 12 6 0 | 0 0 6 18 4 12 12 4 0 | 0 0 4 16 12 1 4 6 4 1 0 | 0 1 5 10 1 .x. ... ... ... ... ... & | 0 2 | * * 210 | 0 0 1 0 4 4 | 0 0 4 4 0 6 12 6 | 0 0 6 18 0 4 12 12 4 | 0 0 4 16 12 0 1 4 6 4 1 | 0 1 5 10 1 ------------------------------+-------+-------------+------------------------+---------------------------------+----------------------------------+---------------------------------------+-------------- o..3x.. ... ... ... ... & | 3 0 | 3 0 0 | 70 * * * * * ♦ 4 0 4 0 0 0 0 0 | 6 0 12 6 0 0 0 0 0 | 4 0 12 12 4 0 0 0 0 0 0 | 1 4 6 5 0 ... x..3o.. ... ... ... & | 3 0 | 3 0 0 | * 280 * * * * | 1 3 0 0 3 0 0 0 | 3 3 3 0 6 3 0 0 0 | 3 1 6 3 0 3 3 1 0 0 0 | 1 3 3 1 1 ox. ... ... ... ... ...&#x & | 1 2 | 0 2 1 | * * 210 * * * ♦ 0 0 4 4 0 0 0 0 | 0 0 6 18 0 0 0 0 0 | 0 0 4 16 12 0 0 0 0 0 0 | 0 1 5 10 0 ... xo. ... ... ... ...&#x & | 2 1 | 1 2 0 | * * * 840 * * | 0 0 1 0 3 3 0 0 | 0 0 3 3 3 6 3 0 0 | 0 0 3 6 3 1 3 3 1 0 0 | 0 1 3 4 1 ... ... ... ... ... ox.&#x & | 1 2 | 0 2 1 | * * * * 840 * | 0 0 0 1 0 3 3 0 | 0 0 0 6 0 3 6 3 0 | 0 0 0 6 6 0 1 3 3 1 0 | 0 0 2 6 1 .x.3.o. ... ... ... ... & | 0 3 | 0 0 3 | * * * * * 280 | 0 0 1 0 0 0 3 3 | 0 0 3 3 0 0 3 6 3 | 0 0 3 6 3 0 0 1 3 3 1 | 0 1 3 4 1 ------------------------------+-------+-------------+------------------------+---------------------------------+----------------------------------+---------------------------------------+-------------- o..3x..3o.. ... ... ... & ♦ 6 0 | 12 0 0 | 4 4 0 0 0 0 | 70 * * * * * * * ♦ 3 0 3 0 0 0 0 0 0 | 3 0 6 3 0 0 0 0 0 0 0 | 1 3 3 1 0 ... x..3o..3o.. ... ... & ♦ 4 0 | 6 0 0 | 0 4 0 0 0 0 | * 210 * * * * * * | 1 2 0 0 2 0 0 0 0 | 2 1 2 0 0 2 1 0 0 0 0 | 1 2 1 0 1 ox.3xo. ... ... ... ...&#x & ♦ 3 3 | 3 6 3 | 1 0 3 3 0 1 | * * 280 * * * * * ♦ 0 0 3 3 0 0 0 0 0 | 0 0 3 6 3 0 0 0 0 0 0 | 0 1 3 4 0 oxo ... ... ... ... oxo&#xt ♦ 2 4 | 0 8 4 | 0 0 4 0 4 0 | * * * 210 * * * * ♦ 0 0 0 6 0 0 0 0 0 | 0 0 0 6 6 0 0 0 0 0 0 | 0 0 2 6 0 ... xo.3oo. ... ... ...&#x & ♦ 3 1 | 3 3 0 | 0 1 0 3 0 0 | * * * * 840 * * * | 0 0 1 0 2 2 0 0 0 | 0 0 2 2 0 1 2 1 0 0 0 | 0 1 2 1 1 ... xo. ... ... ... ox.&#x & ♦ 2 2 | 1 4 1 | 0 0 0 2 2 0 | * * * * * 1260 * * | 0 0 0 1 0 2 2 0 0 | 0 0 0 2 2 0 1 2 1 0 0 | 0 0 1 3 1 ... ... ... ... oo.3ox.&#x & ♦ 1 3 | 0 3 3 | 0 0 0 0 3 1 | * * * * * * 840 * | 0 0 0 1 0 0 2 2 0 | 0 0 0 2 2 0 0 1 2 1 0 | 0 0 1 3 1 .x.3.o.3.o. ... ... ... & ♦ 0 4 | 0 0 6 | 0 0 0 0 0 4 | * * * * * * * 210 | 0 0 1 0 0 0 0 2 2 | 0 0 2 2 0 0 0 0 1 2 1 | 0 1 2 1 1 ------------------------------+-------+-------------+------------------------+---------------------------------+----------------------------------+---------------------------------------+-------------- o..3x..3o..3o.. ... ... & ♦ 10 0 | 30 0 0 | 10 20 0 0 0 0 | 5 5 0 0 0 0 0 0 | 42 * * * * * * * * | 2 0 2 0 0 0 0 0 0 0 0 | 1 2 1 0 0 ... x..3o..3o..3o.. ... & ♦ 5 0 | 10 0 0 | 0 10 0 0 0 0 | 0 5 0 0 0 0 0 0 | * 84 * * * * * * * | 1 1 0 0 0 1 0 0 0 0 0 | 1 1 0 0 1 ox.3xo.3oo. ... ... ...&#x & ♦ 6 4 | 12 12 6 | 4 4 6 12 0 4 | 1 0 4 0 4 0 0 1 | * * 210 * * * * * * | 0 0 2 2 0 0 0 0 0 0 0 | 0 1 2 1 0 oxo3xoo ... ... ... oxo&#xt & ♦ 4 6 | 3 18 9 | 1 0 9 6 12 2 | 0 0 2 3 0 3 2 0 | * * * 420 * * * * * | 0 0 0 2 2 0 0 0 0 0 0 | 0 0 1 3 0 ... xo.3oo.3oo. ... ...&#x & ♦ 4 1 | 6 4 0 | 0 4 0 6 0 0 | 0 1 0 0 4 0 0 0 | * * * * 420 * * * * | 0 0 1 0 0 1 1 0 0 0 0 | 0 1 1 0 1 ... xo.3oo. ... ... ox.&#x & ♦ 3 2 | 3 6 1 | 0 1 0 6 3 0 | 0 0 0 0 2 3 0 0 | * * * * * 840 * * * | 0 0 0 1 0 0 1 1 0 0 0 | 0 0 1 1 1 ... xo. ... ... oo.3ox.&#x & ♦ 2 3 | 1 6 3 | 0 0 0 3 6 1 | 0 0 0 0 0 3 2 0 | * * * * * * 840 * * | 0 0 0 0 1 0 0 1 1 0 0 | 0 0 0 2 1 ... ... ... oo.3oo.3ox.&#x & ♦ 1 4 | 0 4 6 | 0 0 0 0 6 4 | 0 0 0 0 0 0 4 1 | * * * * * * * 420 * | 0 0 0 1 0 0 0 0 1 1 0 | 0 0 1 1 1 .x.3.o.3.o.3.o. ... ... & ♦ 0 5 | 0 0 10 | 0 0 0 0 0 10 | 0 0 0 0 0 0 0 5 | * * * * * * * * 84 | 0 0 1 0 0 0 0 0 0 1 1 | 0 1 1 0 1 ------------------------------+-------+-------------+------------------------+---------------------------------+----------------------------------+---------------------------------------+-------------- o..3x..3o..3o..3o.. ... & ♦ 15 0 | 60 0 0 | 20 60 0 0 0 0 | 15 30 0 0 0 0 0 0 | 6 6 0 0 0 0 0 0 0 | 14 * * * * * * * * * * | 1 1 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 | 0 6 0 0 0 0 0 0 0 | * 14 * * * * * * * * * | 1 0 0 0 1 ox.3xo.3oo.3oo. ... ...&#x & ♦ 10 5 | 30 20 10 | 10 20 10 30 0 10 | 5 5 10 0 20 0 0 5 | 1 0 5 0 5 0 0 0 1 | * * 84 * * * * * * * * | 0 1 1 0 0 oxo3xoo3ooo ... ... oxo&#xt & ♦ 7 8 | 12 32 16 | 4 4 16 24 24 8 | 1 0 8 6 8 12 8 2 | 0 0 2 4 0 4 0 2 0 | * * * 210 * * * * * * * | 0 0 1 1 0 oxo3xoo ... ... oox3oxo&#xt ♦ 6 9 | 6 36 18 | 2 0 18 18 36 6 | 0 0 6 9 0 18 12 0 | 0 0 0 6 0 0 6 0 0 | * * * * 140 * * * * * * | 0 0 0 2 0 ... xo.3oo.3oo.3oo. ...&#x & ♦ 5 1 | 10 5 0 | 0 10 0 10 0 0 | 0 5 0 0 10 0 0 0 | 0 1 0 0 5 0 0 0 0 | * * * * * 84 * * * * * | 0 1 0 0 1 ... xo.3oo.3oo. ... ox.&#x & ♦ 4 2 | 6 8 1 | 0 4 0 12 4 0 | 0 1 0 0 8 6 0 0 | 0 0 0 0 2 4 0 0 0 | * * * * * * 210 * * * * | 0 0 1 0 1 ... xo.3oo. ... oo.3ox.&#x & ♦ 3 3 | 3 9 3 | 0 1 0 9 9 1 | 0 0 0 0 3 9 3 0 | 0 0 0 0 0 3 3 0 0 | * * * * * * * 280 * * * | 0 0 0 1 1 ... xo. ... oo.3oo.3ox.&#x & ♦ 2 4 | 1 8 6 | 0 0 0 4 12 4 | 0 0 0 0 0 6 8 1 | 0 0 0 0 0 0 4 2 0 | * * * * * * * * 210 * * | 0 0 0 1 1 ... ... oo.3oo.3oo.3ox.&#x & ♦ 1 5 | 0 5 10 | 0 0 0 0 10 10 | 0 0 0 0 0 0 10 5 | 0 0 0 0 0 0 0 5 1 | * * * * * * * * * 84 * | 0 0 1 0 1 .x.3.o.3.o.3.o.3.o. ... & ♦ 0 6 | 0 0 15 | 0 0 0 0 0 20 | 0 0 0 0 0 0 0 15 | 0 0 0 0 0 0 0 0 6 | * * * * * * * * * * 14 | 0 1 0 0 1 ------------------------------+-------+-------------+------------------------+---------------------------------+----------------------------------+---------------------------------------+-------------- o..3x..3o..3o..3o..3o.. & ♦ 21 0 | 105 0 0 | 35 140 0 0 0 0 | 35 105 0 0 0 0 0 0 | 21 42 0 0 0 0 0 0 0 | 7 7 0 0 0 0 0 0 0 0 0 | 2 * * * * ox.3xo.3oo.3oo.3oo. ...&#x & ♦ 15 6 | 60 30 15 | 20 60 15 60 0 20 | 15 30 20 0 60 0 0 15 | 6 6 15 0 30 0 0 0 6 | 1 0 6 0 0 6 0 0 0 0 1 | * 14 * * * oxo3xoo3ooo3ooo ... oxo&#xt & ♦ 11 10 | 30 50 25 | 10 20 25 60 40 20 | 5 5 20 10 40 30 20 10 | 1 0 10 10 10 20 0 10 2 | 0 0 2 5 0 0 5 0 0 2 0 | * * 42 * * oxo3xoo3ooo ... oox3oxo&#xt & ♦ 9 12 | 15 60 30 | 5 4 30 48 72 16 | 1 0 16 18 12 54 36 3 | 0 0 3 18 0 12 24 6 0 | 0 0 0 3 4 0 0 4 3 0 0 | * * * 70 * ... xo.3oo.3oo.3oo.3ox.&#x & ♦ 6 6 | 15 30 15 | 0 20 0 60 60 20 | 0 15 0 0 60 90 60 15 | 0 6 0 0 30 60 60 30 6 | 0 1 0 0 0 6 15 20 15 6 1 | * * * * 14
ox(xo)ox3xo(xo)xo oo(oo)oo3oo(ox)oo3oo(oo)oo *d3ox(oo)xo&#xt → all heights = 1/sqrt(6) = 0.408248 ({3} || pseudo dual trahex || pseudo compound of {6} and perp ico || pseudo trahex || dual {3}) o.(..)..3o.(..).. o.(..)..3o.(..)..3o.(..).. *d3o.(..).. & | 6 * * * ♦ 2 16 2 0 0 0 0 0 0 0 | 1 8 16 48 16 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 8 48 64 48 8 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 64 16 16 64 24 24 32 0 0 0 0 0 0 0 0 0 0 0 0 | 16 16 16 16 32 32 8 8 0 0 0 0 0 0 0 0 | 2 8 8 8 8 0 .o(..)..3.o(..).. .o(..)..3.o(..)..3.o(..).. *d3.o(..).. & | * 48 * * ♦ 0 2 0 2 6 2 6 2 0 0 | 0 2 1 12 2 0 1 12 1 12 2 12 12 12 6 3 0 0 0 | 1 6 24 12 3 12 4 4 6 24 12 6 24 4 4 12 18 24 0 0 | 12 8 8 24 18 6 24 12 8 8 24 12 8 8 4 4 36 8 8 | 4 4 8 8 36 12 8 8 4 4 8 8 4 4 12 12 | 1 4 4 12 12 1 ..(o.)..3..(o.).. ..(o.)..3..(o.)..3..(o.).. *d3..(o.).. | * * 6 * ♦ 0 0 2 0 0 16 0 0 2 0 | 0 0 0 0 16 2 0 0 16 48 8 0 0 0 0 0 0 0 0 | 0 0 0 48 16 0 0 0 48 64 24 0 0 0 0 0 0 0 0 0 | 0 0 0 64 48 0 0 64 16 16 32 0 0 0 0 0 0 0 0 | 0 0 16 16 64 0 0 0 16 16 8 8 0 0 0 0 | 2 0 0 16 16 0 ..(.o)..3..(.o).. ..(.o)..3..(.o)..3..(.o).. *d3..(.o).. | * * * 24 ♦ 0 0 0 0 0 0 12 0 0 8 | 0 0 0 0 0 0 0 0 0 0 0 12 12 48 6 0 4 4 4 | 0 0 0 0 0 6 0 0 0 0 6 4 48 24 24 24 12 48 2 2 | 0 0 0 0 6 2 24 0 0 0 24 16 24 24 12 12 48 24 24 | 0 0 0 0 24 8 12 12 0 0 12 12 8 8 24 24 | 0 4 4 12 12 2 ---------------------------------------------------------------+-----------+-------------------------------+---------------------------------------------------------------+------------------------------------------------------------------------+----------------------------------------------------------------------+----------------------------------------------------+---------------- ..(..).. x.(..).. ..(..).. ..(..).. ..(..).. ..(..).. & | 2 0 0 0 | 6 * * * * * * * * * | 1 0 8 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 8 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 32 0 0 0 0 24 0 0 0 0 0 0 0 0 0 0 0 0 0 | 8 8 0 0 0 32 0 0 0 0 0 0 0 0 0 0 | 1 8 8 0 0 0 oo(..)..3oo(..).. oo(..)..3oo(..)..3oo(..).. *d3oo(..)..&#x & | 1 1 0 0 | * 96 * * * * * * * * | 0 1 1 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 6 12 6 1 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 12 4 4 12 6 6 12 0 0 0 0 0 0 0 0 0 0 0 0 | 4 4 4 4 12 12 4 4 0 0 0 0 0 0 0 0 | 1 4 4 4 4 0 o.(o.)..3o.(o.).. o.(o.)..3o.(o.)..3o.(o.).. *d3o.(o.)..&#x & | 1 0 1 0 | * * 12 * * * * * * * | 0 0 0 0 8 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 24 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 32 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 8 8 32 0 0 0 0 0 0 0 0 0 0 0 | 1 0 0 8 8 0 .x(..).. ..(..).. ..(..).. ..(..).. ..(..).. ..(..).. & | 0 2 0 0 | * * * 48 * * * * * * | 0 1 0 0 0 0 1 0 0 0 0 0 6 0 0 1 0 0 0 | 1 0 0 0 1 6 0 0 0 0 0 6 12 0 0 0 6 0 0 0 | 0 0 0 0 6 6 12 0 0 0 0 12 4 4 0 0 12 0 0 | 0 0 0 0 12 12 4 4 0 0 0 0 4 4 4 4 | 0 4 4 4 4 1 ..(..).. ..(..).. ..(..).. ..(..).. ..(..).. .x(..).. & | 0 2 0 0 | * * * * 144 * * * * * | 0 0 0 2 0 0 0 4 0 2 0 0 0 0 1 0 0 0 0 | 0 1 8 2 0 2 2 2 1 8 2 0 0 0 0 4 0 0 0 0 | 4 4 4 8 3 1 8 4 4 4 8 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* * * | 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 | 1 0 0 0 2 0 ..(..).. ..(..).. ..(..).. .o(ox)o. ..(..).. *d3.x(oo)x.&#xr ♦ 0 6 1 3 | 0 0 0 0 6 6 12 3 0 3 | 0 0 0 0 0 0 0 2 0 6 3 6 0 6 6 0 0 0 1 | 0 0 0 0 0 0 0 0 0 2 3 0 0 0 0 2 0 3 0 0 | * * * * * * * * * * 192 * * * * * * * * | 0 0 0 0 2 0 0 0 0 0 1 1 0 0 0 0 | 0 0 0 2 2 0 cycle (BDEC) .x(.o)..3.o(.o).. ..(..).. .o(.x).. ..(..).. ..(..)..&#x & ♦ 0 3 0 2 | 0 0 0 3 0 0 6 0 0 1 | 0 0 0 0 0 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 | * * * * * * * * * * * 192 * * * * * * * | 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1 .x(.o).. ..(..).. .o(.o)..3.o(.x).. ..(..).. ..(..)..&#x & ♦ 0 2 0 3 | 0 0 0 1 0 0 6 0 0 3 | 0 0 0 0 0 0 0 0 0 0 0 0 3 6 0 0 1 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 0 0 0 0 0 | * * * * * * * * * * * * 192 * * * * * * | 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1 .x(.o).. ..(..).. ..(..).. .o(.x)..3.o(.o).. ..(..)..&#x & ♦ 0 2 0 3 | 0 0 0 1 0 0 6 0 0 3 | 0 0 0 0 0 0 0 0 0 0 0 0 3 6 0 0 0 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 3 0 2 0 0 0 0 0 | * * * * * * * * * * * * * 192 * * * * * | 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 | 0 0 1 0 1 1 ..(..).. ..(..).. .o(.o)..3.o(.x).. ..(..).. *d3.x(.o)..&#x & ♦ 0 4 0 6 | 0 0 0 0 6 0 12 0 0 12 | 0 0 0 0 0 0 0 4 0 0 0 0 0 12 6 0 4 0 4 | 0 0 0 0 0 0 1 0 0 0 0 0 0 4 0 4 0 0 1 0 | * * * * * * * * * * * * * * 48 * * * * | 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 | 0 1 0 3 0 0 ..(..).. ..(..).. ..(..).. .o(.x)..3.o(.o).. *d3.x(.o)..&#x & ♦ 0 4 0 6 | 0 0 0 0 6 0 12 0 0 12 | 0 0 0 0 0 0 0 4 0 0 0 0 0 12 6 0 0 4 4 | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 4 4 0 0 0 1 | * * * * * * * * * * * * * * * 48 * * * | 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 | 0 0 1 0 3 0 .x(.o)o. ..(..).. ..(..).. .o(.x)o. ..(..).. ..(..)..&#x & ♦ 0 3 0 2 | 0 0 0 1 0 0 6 2 0 1 | 0 0 0 0 0 0 0 0 0 0 0 4 2 3 0 1 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 2 0 0 | * * * * * * * * * * * * * * * * 576 * * | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 | 0 0 0 1 1 1 ..(..).. ..(..).. .o(.o)o.3.o(.x)o. ..(..).. ..(..)..&#x ♦ 0 2 0 3 | 0 0 0 0 0 0 6 1 0 3 | 0 0 0 0 0 0 0 0 0 0 0 3 0 6 0 0 1 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 3 0 0 | * * * * * * * * * * * * * * * * * 192 * | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 0 | 0 0 0 2 0 1 ..(..).. ..(..).. ..(..).. .o(.x)o.3.o(.o)o. ..(..)..&#x ♦ 0 2 0 3 | 0 0 0 0 0 0 6 1 0 3 | 0 0 0 0 0 0 0 0 0 0 0 3 0 6 0 0 0 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 3 0 0 | * * * * * * * * * * * * * * * * * * 192 | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 | 0 0 0 0 2 1 ---------------------------------------------------------------+-----------+-------------------------------+---------------------------------------------------------------+------------------------------------------------------------------------+----------------------------------------------------------------------+----------------------------------------------------+---------------- ..(..).. xo(..).. oo(..)..3oo(..).. ..(..).. *d3ox(..)..&#x & ♦ 2 4 0 0 | 1 8 0 0 6 0 0 0 0 0 | 0 0 4 12 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 | 0 6 8 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 48 * * * * * * * * * * * * * * * | 1 1 0 0 0 0 ..(..).. xo(..).. ..(..).. oo(..)..3oo(..).. *d3ox(..)..&#x & ♦ 2 4 0 0 | 1 8 0 0 6 0 0 0 0 0 | 0 0 4 12 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 | 0 6 8 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | 4 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | * 48 * * * * * * * * * * * * * * | 1 0 1 0 0 0 ..(..).. ..(..).. oo(o.)..3oo(o.).. ..(..).. *d3ox(o.)..&#x & ♦ 1 4 1 0 | 0 4 1 0 6 4 0 0 0 0 | 0 0 0 6 4 0 0 4 0 6 0 0 0 0 0 0 0 0 0 | 0 0 4 6 0 0 1 0 0 4 0 0 0 0 0 0 0 0 0 0 | 0 1 0 4 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | * * 96 * * * * * * * * * * * * * | 1 0 0 1 0 0 ..(..).. ..(..).. ..(..).. oo(o.)..3oo(o.).. *d3ox(o.)..&#x & ♦ 1 4 1 0 | 0 4 1 0 6 4 0 0 0 0 | 0 0 0 6 4 0 0 4 0 6 0 0 0 0 0 0 0 0 0 | 0 0 4 6 0 0 0 1 0 4 0 0 0 0 0 0 0 0 0 0 | 0 0 1 4 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | * * * 96 * * * * * * * * * * * * | 1 0 0 0 1 0 ox(xo)o. ..(..).. ..(..).. oo(ox)o. ..(..).. *d3ox(oo)x.&#xr & ♦ 1 9 2 3 | 0 6 2 3 9 12 18 6 1 3 | 0 3 0 6 6 1 0 3 3 12 6 12 6 9 9 3 0 0 1 | 0 0 2 6 3 3 0 0 3 4 6 0 3 0 0 3 6 6 0 0 | 0 0 0 2 3 0 1 1 0 0 2 0 0 0 0 0 3 0 0 | * * * * 192 * * * * * * * * * * * | 0 0 0 1 1 0 cycle(ABDEC) ox(.o)..3xo(.o).. ..(..).. oo(.x).. ..(..).. *d3ox(.o)..&#xt & ♦ 3 9 0 3 | 3 18 0 9 9 0 18 0 0 3 | 1 9 9 18 0 0 3 3 0 0 0 0 18 9 9 0 0 0 1 | 3 9 6 0 0 9 0 0 0 0 0 6 9 0 0 3 0 0 0 0 | 3 0 0 0 0 3 3 0 0 0 0 3 0 0 0 0 0 0 0 | * * * * * 64 * * * * * * * * * * | 0 1 1 0 0 0 ox(.o).. ..(..).. oo(.o)..3oo(.x).. ..(..).. *d3ox(.o)..&#xt & ♦ 1 8 0 6 | 0 8 0 4 12 0 24 0 0 12 | 0 4 0 12 0 0 0 8 0 0 0 0 12 24 12 0 4 0 4 | 0 0 8 0 0 6 2 0 0 0 0 0 12 8 0 8 0 0 1 0 | 0 2 0 0 0 0 4 0 0 0 0 0 4 0 2 0 0 0 0 | * * * * * * 48 * * * * * * * * * | 0 1 0 1 0 0 ox(.o).. ..(..).. ..(..).. oo(.x)..3oo(.o).. *d3ox(.o)..&#xt & ♦ 1 8 0 6 | 0 8 0 4 12 0 24 0 0 12 | 0 4 0 12 0 0 0 8 0 0 0 0 12 24 12 0 0 4 4 | 0 0 8 0 0 6 0 2 0 0 0 0 12 0 8 8 0 0 0 1 | 0 0 2 0 0 0 4 0 0 0 0 0 0 4 0 2 0 0 0 | * * * * * * * 48 * * * * * * * * | 0 0 1 0 1 0 ..(..).. .o(x.).. .o(o.)..3.o(o.).. ..(..).. *d3.x(o.)..&#x & ♦ 0 4 2 0 | 0 0 0 0 6 8 0 0 1 0 | 0 0 0 0 0 0 0 4 4 12 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 1 0 6 8 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 4 2 0 0 0 0 0 0 0 0 0 0 | * * * * * * * * 48 * * * * * * * | 1 0 0 1 0 0 ..(..).. .o(x.).. ..(..).. .o(o.)..3.o(o.).. *d3.x(o.)..&#x & ♦ 0 4 2 0 | 0 0 0 0 6 8 0 0 1 0 | 0 0 0 0 0 0 0 4 4 12 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 1 6 8 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 4 0 2 0 0 0 0 0 0 0 0 0 | * * * * * * * * * 48 * * * * * * | 1 0 0 0 1 0 ..(..).. ..(..).. .o(oo)o.3.o(ox)o. ..(..).. *d3.x(oo)x.&#xt ♦ 0 8 1 6 | 0 0 0 0 12 8 24 4 0 12 | 0 0 0 0 0 0 0 8 0 12 4 12 0 24 12 0 4 0 4 | 0 0 0 0 0 0 2 0 0 8 6 0 0 8 0 8 0 12 1 0 | 0 0 0 0 0 0 0 0 2 0 4 0 0 0 2 0 0 4 0 | * * * * * * * * * * 48 * * * * * | 0 0 0 2 0 0 ..(..).. ..(..).. ..(..).. .o(ox)o.3.o(oo)o. *d3.x(oo)x.&#xt ♦ 0 8 1 6 | 0 0 0 0 12 8 24 4 0 12 | 0 0 0 0 0 0 0 8 0 12 4 12 0 24 12 0 0 4 4 | 0 0 0 0 0 0 0 2 0 8 6 0 0 0 8 8 0 12 0 1 | 0 0 0 0 0 0 0 0 0 2 4 0 0 0 0 2 0 0 4 | * * * * * * * * * * * 48 * * * * | 0 0 0 0 2 0 .x(.o)..3.o(.o).. .o(.o)..3.o(.x).. ..(..).. ..(..)..&#x & ♦ 0 3 0 3 | 0 0 0 3 0 0 9 0 0 3 | 0 0 0 0 0 0 1 0 0 0 0 0 9 9 0 0 1 0 0 | 0 0 0 0 0 0 0 0 0 0 0 3 9 3 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 3 3 0 0 0 0 0 0 | * * * * * * * * * * * * 64 * * * | 0 1 0 0 0 1 .x(.o)..3.o(.o).. ..(..).. .o(.x)..3.o(.o).. ..(..)..&#x & ♦ 0 3 0 3 | 0 0 0 3 0 0 9 0 0 3 | 0 0 0 0 0 0 1 0 0 0 0 0 9 9 0 0 0 1 0 | 0 0 0 0 0 0 0 0 0 0 0 3 9 0 3 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 3 0 3 0 0 0 0 0 | * * * * * * * * * * * * * 64 * * | 0 0 1 0 0 1 .x(.o)o. ..(..).. .o(.o)o.3.o(.x)o. ..(..).. ..(..)..&#x & ♦ 0 3 0 3 | 0 0 0 1 0 0 9 2 0 3 | 0 0 0 0 0 0 0 0 0 0 0 6 3 9 0 1 1 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 3 3 0 0 3 6 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 3 2 0 | * * * * * * * * * * * * * * 192 * | 0 0 0 1 0 1 .x(.o)o. ..(..).. ..(..).. .o(.x)o.3.o(.o)o. ..(..)..&#x & ♦ 0 3 0 3 | 0 0 0 1 0 0 9 2 0 3 | 0 0 0 0 0 0 0 0 0 0 0 6 3 9 0 1 0 1 0 | 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 0 3 6 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 3 0 2 | * * * * * * * * * * * * * * * 192 | 0 0 0 0 1 1 ---------------------------------------------------------------+-----------+-------------------------------+---------------------------------------------------------------+------------------------------------------------------------------------+----------------------------------------------------------------------+----------------------------------------------------+---------------- ..(..).. xo(x.).. oo(o.)..3oo(o.)..3oo(o.).. *d3ox(o.)..&#xt & ♦ 2 8 2 0 | 1 16 2 0 24 16 0 0 1 0 | 0 0 8 48 16 0 0 32 8 48 0 0 0 0 0 0 0 0 0 | 0 24 64 48 0 0 8 8 24 64 0 0 0 0 0 0 0 0 0 0 | 32 16 16 64 0 0 0 32 16 16 0 0 0 0 0 0 0 0 0 | 8 8 16 16 0 0 0 0 8 8 0 0 0 0 0 0 | 6 * * * * * ox(.o)..3xo(.o).. oo(.o)..3oo(.x).. ..(..).. *d3ox(.o)..&#xt & ♦ 3 12 0 6 | 3 24 0 12 18 0 36 0 0 12 | 1 12 12 36 0 0 4 12 0 0 0 0 36 36 18 0 4 0 4 | 4 18 24 0 0 18 3 0 0 0 0 12 36 12 0 12 0 0 1 0 | 12 6 0 0 0 6 12 0 0 0 0 12 12 0 3 0 0 0 0 | 3 0 0 0 0 4 3 0 0 0 0 0 4 0 0 0 | * 16 * * * * ox(.o)..3xo(.o).. ..(..).. oo(.x)..3oo(.o).. *d3ox(.o)..&#xt & ♦ 3 12 0 6 | 3 24 0 12 18 0 36 0 0 12 | 1 12 12 36 0 0 4 12 0 0 0 0 36 36 18 0 0 4 4 | 4 18 24 0 0 18 0 3 0 0 0 12 36 0 12 12 0 0 0 1 | 12 0 6 0 0 6 12 0 0 0 0 12 0 12 0 3 0 0 0 | 0 3 0 0 0 4 0 3 0 0 0 0 0 4 0 0 | * * 16 * * * ox(xo)o. ..(..).. oo(oo)o.3oo(ox)o. ..(..).. *d3ox(oo)x.&#xr & ♦ 1 12 2 6 | 0 8 2 4 18 16 36 8 1 12 | 0 4 0 12 8 1 0 12 4 24 8 24 12 36 18 4 4 0 4 | 0 0 8 12 4 6 3 0 6 16 12 0 12 12 0 12 12 24 1 0 | 0 2 0 8 6 0 4 4 4 0 8 0 4 0 3 0 12 8 0 | 0 0 2 0 4 0 1 0 1 0 2 0 0 0 4 0 | * * * 48 * * cycle(ABDEC) ox(xo)o. ..(..).. ..(..).. oo(ox)o.3oo(oo)o. *d3ox(oo)x.&#xr & ♦ 1 12 2 6 | 0 8 2 4 18 16 36 8 1 12 | 0 4 0 12 8 1 0 12 4 24 8 24 12 36 18 4 0 4 4 | 0 0 8 12 4 6 0 3 6 16 12 0 12 0 12 12 12 24 0 1 | 0 0 2 8 6 0 4 4 0 4 8 0 0 4 0 3 12 0 8 | 0 0 0 2 4 0 0 1 0 1 0 2 0 0 0 4 | * * * * 48 * cycle(ABDEC) .x(.o)o.3.o(.o)x. .o(.o)o.3.o(.x)o.3.o(.o)o. ..(..)..&#xt ♦ 0 6 0 6 | 0 0 0 6 0 0 36 6 0 12 | 0 0 0 0 0 0 2 0 0 0 0 36 36 72 0 6 4 4 0 | 0 0 0 0 0 0 0 0 0 0 0 12 72 24 24 0 36 72 0 0 | 0 0 0 0 0 0 0 0 0 0 0 24 24 24 0 0 72 24 24 | 0 0 0 0 0 0 0 0 0 0 0 0 8 8 24 24 | * * * * * 8
oxo3xoo3ooo4ooo oxo3oox4ooo&#zx → all existing heights = 0 (tegum sum of ico, octahex, and perp co) o..3o..3o..4o.. o..3o..4o.. | 24 * * ♦ 8 12 0 0 0 0 | 4 8 6 48 24 0 0 0 0 0 0 | 4 24 12 48 96 16 0 0 0 0 | 24 48 8 96 64 0 0 | 48 32 64 0 | 32 2 0 .o.3.o.3.o.4.o. .o.3.o.4.o. | * 48 * ♦ 0 6 6 4 4 0 | 0 0 6 12 24 12 4 24 4 4 0 | 0 12 24 8 48 24 8 48 24 4 | 8 48 24 32 48 32 48 | 32 48 32 32 | 32 1 1 ..o3..o3..o4..o ..o3..o4..o | * * 12 ♦ 0 0 0 0 16 4 | 0 0 0 0 0 0 0 48 8 32 2 | 0 0 24 0 0 0 0 64 96 16 | 0 32 48 0 0 32 128 | 16 64 0 64 | 32 0 2 --------------------------------+----------+----------------------+---------------------------------------+---------------------------------------+----------------------------+-----------------+-------- ... x.. ... ... ... ... ... | 2 0 0 | 96 * * * * * | 1 2 0 6 0 0 0 0 0 0 0 | 2 6 0 12 12 0 0 0 0 0 | 12 12 0 24 8 0 0 | 24 8 16 0 | 16 1 0 oo.3oo.3oo.4oo. oo.3oo.4oo.&#x | 1 1 0 | * 288 * * * * | 0 0 1 4 4 0 0 0 0 0 0 | 0 4 4 4 16 4 0 0 0 0 | 4 16 4 16 16 0 0 | 16 16 16 0 | 16 1 0 .x. ... ... ... ... ... ... | 0 2 0 | * * 144 * * * | 0 0 1 0 0 4 0 4 0 0 0 | 0 4 4 0 0 0 4 16 4 0 | 4 16 4 0 0 16 16 | 16 16 0 16 | 16 0 1 ... ... ... ... .x. ... ... | 0 2 0 | * * * 96 * * | 0 0 0 0 6 0 2 0 1 0 0 | 0 0 6 0 12 12 0 0 0 2 | 0 12 12 8 24 0 0 | 8 24 16 0 | 16 1 0 .oo3.oo3.oo4.oo .oo3.oo4.oo&#x | 0 1 1 | * * * * 192 * | 0 0 0 0 0 0 0 6 1 2 0 | 0 0 6 0 0 0 0 12 12 2 | 0 12 12 0 0 8 24 | 8 24 0 16 | 16 0 1 ... ... ... ... ... ..x ... | 0 0 2 | * * * * * 24 | 0 0 0 0 0 0 0 0 0 8 1 | 0 0 0 0 0 0 0 0 24 8 | 0 0 24 0 0 0 32 | 0 32 0 16 | 16 0 1 --------------------------------+----------+----------------------+---------------------------------------+---------------------------------------+----------------------------+-----------------+-------- o..3x.. ... ... ... ... ... | 3 0 0 | 3 0 0 0 0 0 | 32 * * * * * * * * * * ♦ 2 6 0 0 0 0 0 0 0 0 | 12 12 0 0 0 0 0 | 24 8 0 0 | 16 0 0 ... x..3o.. ... ... ... ... | 3 0 0 | 3 0 0 0 0 0 | * 64 * * * * * * * * * | 1 0 0 6 0 0 0 0 0 0 | 6 0 0 12 0 0 0 | 12 0 8 0 | 8 1 0 ox. ... ... ... ... ... ...&#x | 1 2 0 | 0 2 1 0 0 0 | * * 144 * * * * * * * * ♦ 0 4 4 0 0 0 0 0 0 0 | 4 16 4 0 0 0 0 | 16 16 0 0 | 16 0 0 ... xo. ... ... ... ... ...&#x | 2 1 0 | 1 2 0 0 0 0 | * * * 576 * * * * * * * | 0 1 0 2 4 0 0 0 0 0 | 2 4 0 8 4 0 0 | 8 4 8 0 | 8 1 0 ... ... ... ... ox. ... ...&#x | 1 2 0 | 0 2 0 1 0 0 | * * * * 576 * * * * * * | 0 0 1 0 4 2 0 0 0 0 | 0 4 2 4 8 0 0 | 4 8 8 0 | 8 1 0 .x.3.o. ... ... ... ... ... | 0 3 0 | 0 0 3 0 0 0 | * * * * * 192 * * * * * | 0 1 0 0 0 0 2 4 0 0 | 2 4 0 0 0 8 4 | 8 4 0 8 | 8 0 1 ... ... ... ... .x.3.o. ... | 0 3 0 | 0 0 0 3 0 0 | * * * * * * 64 * * * * | 0 0 0 0 0 6 0 0 0 1 | 0 0 6 0 12 0 0 | 0 12 8 0 | 8 1 0 .xo ... ... ... ... ... ...&#x | 0 2 1 | 0 0 1 0 2 0 | * * * * * * * 576 * * * | 0 0 1 0 0 0 0 4 2 0 | 0 4 2 0 0 4 8 | 4 8 0 8 | 8 0 1 ... ... ... ... .xo ... ...&#x | 0 2 1 | 0 0 0 1 2 0 | * * * * * * * * 96 * * ♦ 0 0 6 0 0 0 0 0 0 2 | 0 12 12 0 0 0 0 | 8 24 0 0 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0 | 4 0 4 0 | 4 1 0 ... xo. ... ... ox. ... ...&#x ♦ 2 2 0 | 1 4 0 1 0 0 | 0 0 0 2 2 0 0 0 0 0 0 | * * * * 1152 * * * * * | 0 1 0 2 2 0 0 | 2 2 4 0 | 4 1 0 ... ... ... ... ox.3oo. ...&#x ♦ 1 3 0 | 0 3 0 3 0 0 | 0 0 0 0 3 0 1 0 0 0 0 | * * * * * 384 * * * * | 0 0 1 0 4 0 0 | 0 4 4 0 | 4 1 0 .x.3.o.3.o. ... ... ... ... ♦ 0 4 0 | 0 0 6 0 0 0 | 0 0 0 0 0 4 0 0 0 0 0 | * * * * * * 96 * * * | 1 0 0 0 0 4 0 | 4 0 0 4 | 4 0 1 .xo3.oo ... ... ... ... ...&#x ♦ 0 3 1 | 0 0 3 0 3 0 | 0 0 0 0 0 1 0 3 0 0 0 | * * * * * * * 768 * * | 0 1 0 0 0 2 2 | 2 2 0 4 | 4 0 1 .xo ... ... ... ... .ox ...&#x ♦ 0 2 2 | 0 0 1 0 4 1 | 0 0 0 0 0 0 0 2 0 2 0 | * * * * * * * * 576 * | 0 0 1 0 0 0 4 | 0 4 0 4 | 4 0 1 ... ... ... ... .xo3.ox ...&#x ♦ 0 3 3 | 0 0 0 3 6 3 | 0 0 0 0 0 0 1 0 3 3 1 | * * * * * * * * * 64 | 0 0 6 0 0 0 0 | 0 12 0 0 | 8 0 0 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* * * * | 1 0 1 0 0 0 oxo3xoo ... ... ... oxo3oox&#xt ♦ 3 9 3 | 3 18 9 9 18 0 3 | 1 0 0 9 9 18 3 0 3 18 0 9 9 0 1 | 0 0 3 9 0 0 9 0 6 0 0 6 0 9 0 3 | 0 0 3 0 3 0 0 0 3 0 0 0 3 | * * * 128 * * * * * * * * | 0 1 0 1 0 0 ... xo.3oo. ... oo.3ox. ...&#x ♦ 3 3 0 | 3 9 0 3 0 0 0 | 0 1 0 0 9 9 0 1 0 0 0 0 0 0 0 | 0 0 0 0 3 0 9 3 0 0 0 0 0 0 0 0 | 0 0 0 0 0 3 0 3 0 0 0 0 0 | * * * * 128 * * * * * * * | 1 0 0 0 1 0 ... xo.3oo. ... ... ox.3oo.&#x ♦ 3 3 0 | 3 9 0 3 0 0 0 | 0 1 0 0 9 9 0 0 1 0 0 0 0 0 0 | 0 0 0 0 3 0 9 0 3 0 0 0 0 0 0 0 | 0 0 0 0 0 3 0 0 3 0 0 0 0 | * * * * * 128 * * * * * * | 0 1 0 0 1 0 ... xo. ... *b3oo. oo.3ox. ...&#x ♦ 3 3 0 | 3 9 0 3 0 0 0 | 0 0 1 0 9 9 0 1 0 0 0 0 0 0 0 | 0 0 0 0 0 3 9 3 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 3 3 0 0 0 0 0 | * * * * * * 128 * * * * * | 0 0 1 0 1 0 ... xo. ... *b3oo. ... ox.3oo.&#x ♦ 3 3 0 | 3 9 0 3 0 0 0 | 0 0 1 0 9 9 0 0 1 0 0 0 0 0 0 | 0 0 0 0 0 3 9 0 3 0 0 0 0 0 0 0 | 0 0 0 0 0 0 3 0 3 0 0 0 0 | * * * * * * * 128 * * * * | 0 0 0 1 1 0 .xo3.oo3.oo ... .ox ... ...&#x ♦ 0 4 2 | 0 0 6 0 8 1 0 | 0 0 0 0 0 0 4 0 0 12 4 0 0 0 0 | 0 0 0 0 0 0 0 0 0 1 0 8 6 0 0 0 | 0 0 0 0 0 0 0 0 0 2 0 4 0 | * * * * * * * * 96 * * * | 1 0 0 0 0 1 .xo3.oo3.oo ... ... ... .ox&#x ♦ 0 4 2 | 0 0 6 0 8 0 1 | 0 0 0 0 0 0 4 0 0 12 0 0 4 0 0 | 0 0 0 0 0 0 0 0 0 1 0 8 0 6 0 0 | 0 0 0 0 0 0 0 0 0 2 0 0 4 | * * * * * * * * * 96 * * | 0 1 0 0 0 1 .xo3.oo ... *b3.oo .ox ... ...&#x ♦ 0 4 2 | 0 0 6 0 8 1 0 | 0 0 0 0 0 0 4 0 0 12 4 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 1 8 6 0 0 0 | 0 0 0 0 0 0 0 0 0 0 2 4 0 | * * * * * * * * * * 96 * | 0 0 1 0 0 1 .xo3.oo ... *b3.oo ... ... .ox&#x ♦ 0 4 2 | 0 0 6 0 8 0 1 | 0 0 0 0 0 0 4 0 0 12 0 0 4 0 0 | 0 0 0 0 0 0 0 0 0 0 1 8 0 6 0 0 | 0 0 0 0 0 0 0 0 0 0 2 0 4 | * * * * * * * * * * * 96 | 0 0 0 1 0 1 -----------------------------------+----------+-------------------------+-------------------------------------------------+----------------------------------------------------------+-------------------------------------------------+-------------------------------------------+---------------- oxo3xoo3ooo ... oox3oxo ...&#xt ♦ 6 12 3 | 12 36 18 12 24 3 0 | 4 4 0 18 36 36 12 4 0 36 12 12 0 1 0 | 1 0 12 18 12 0 36 12 0 3 0 24 18 0 4 0 | 3 0 12 6 0 12 0 12 0 6 0 12 0 | 3 0 4 0 4 0 0 0 3 0 0 0 | 32 * * * * * oxo3xoo3ooo ... ... oxo3oox&#xt ♦ 6 12 3 | 12 36 18 12 24 0 3 | 4 4 0 18 36 36 12 0 4 36 0 12 12 0 1 | 1 0 12 18 12 0 36 0 12 3 0 24 0 18 0 4 | 3 0 12 0 6 12 0 0 12 6 0 0 12 | 3 0 0 4 0 4 0 0 0 3 0 0 | * 32 * * * * oxo3xoo ... *b3ooo oox3oxo ...&#xt ♦ 6 12 3 | 12 36 18 12 24 3 0 | 4 0 4 18 36 36 12 4 0 36 12 12 0 1 0 | 0 1 12 18 0 12 36 12 0 0 3 24 18 0 4 0 | 0 3 12 6 0 0 12 12 0 0 6 12 0 | 0 3 4 0 0 0 4 0 0 0 3 0 | * * 32 * * * oxo3xoo ... *b3ooo ... oxo3oox&#xt ♦ 6 12 3 | 12 36 18 12 24 0 3 | 4 0 4 18 36 36 12 0 4 36 0 12 12 0 1 | 0 1 12 18 0 12 36 0 12 0 3 24 0 18 0 4 | 0 3 12 0 6 0 12 0 12 0 6 0 12 | 0 3 0 4 0 0 0 4 0 0 0 3 | * * * 32 * * ... xo.3oo. *b3oo. oo.3ox.3oo.&#zx ♦ 6 6 0 | 12 36 0 12 0 0 0 | 0 4 4 0 72 72 0 4 4 0 0 0 0 0 0 | 0 0 0 0 24 24 144 24 24 0 0 0 0 0 0 0 | 0 0 0 0 0 48 48 48 48 0 0 0 0 | 0 0 0 0 16 16 16 16 0 0 0 0 | * * * * 8 * .xo3.oo3.oo *b3.oo .ox ... .ox&#zx ♦ 0 8 4 | 0 0 24 0 32 2 2 | 0 0 0 0 0 0 32 0 0 96 16 0 16 0 0 | 0 0 0 0 0 0 0 0 0 8 8 128 48 48 0 0 | 0 0 0 0 0 0 0 0 0 32 32 64 64 | 0 0 0 0 0 0 0 0 16 16 16 16 | * * * * * 6
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