Acronym | thexgyt (alt.: pex tedjak) |
Name |
truncated-hexadecachoral gyrotrigonism, partially expanded tridiminished icosiheptaheptacontidipeton, partially expanded tridiminished 21,2 |
Circumradius | sqrt(8/3) = 1.632993 |
Lace city in approx. ASCII-art |
where: E E = o3x3x *b3o (thex) X O = o3x3o *b3x O X = x3x3o *b3o |
Face vector | 144, 648, 1056, 816, 315, 51 |
Confer |
|
By means of a (partial) Stott contraction at the central node positions, applied simultanuously to all layers, this polypeton would reduce to tedjak, the tri-diminishing of the Gosset polytope jak.
Incidence matrix according to Dynkin symbol
xoo3xxx3oxo *b3oox&#x → all pairwise heights = 1/sqrt(2) = 0.707107 o..3o..3o.. *b3o.. & | 144 | 1 4 4 | 4 4 6 8 4 | 4 1 12 2 4 8 4 | 1 4 6 8 5 | 2 5 1 ------------------------+-----+------------+--------------------+------------------------+----------------+-------- x.. ... ... ... & | 2 | 72 * * | 4 0 4 0 0 | 4 0 8 2 0 4 0 | 1 4 4 4 4 | 2 4 1 ... x.. ... ... & | 2 | * 288 * | 1 2 0 2 0 | 2 1 4 0 2 0 1 | 1 2 4 3 0 | 2 3 0 oo.3oo.3oo. *b3oo.&#x & | 2 | * * 288 | 0 0 2 2 2 | 0 0 4 1 1 5 2 | 0 2 2 5 4 | 1 4 1 ------------------------+-----+------------+--------------------+------------------------+----------------+-------- x..3x.. ... ... & | 6 | 3 3 0 | 96 * * * * | 2 0 2 0 0 0 0 | 1 2 2 1 0 | 2 2 0 ... x..3o.. ... & | 3 | 0 3 0 | * 192 * * * | 1 1 1 0 1 0 0 | 1 1 3 1 0 | 2 2 0 xo. ... ... ...&#x & | 3 | 1 0 2 | * * 288 * * | 0 0 2 1 0 2 0 | 0 2 1 2 3 | 1 3 1 ... xx. ... ...&#x & | 4 | 0 2 2 | * * * 288 * | 0 0 2 0 1 0 1 | 0 1 2 3 0 | 1 3 0 ooo3ooo3ooo *b3ooo&#x | 3 | 0 0 3 | * * * * 192 | 0 0 0 0 0 3 1 | 0 0 0 3 3 | 0 3 1 ------------------------+-----+------------+--------------------+------------------------+----------------+-------- x..3x..3o.. ... & ♦ 12 | 6 12 0 | 4 4 0 0 0 | 48 * * * * * * | 1 1 1 0 0 | 2 1 0 ... x..3o.. *b3o.. & ♦ 6 | 0 12 0 | 0 8 0 0 0 | * 24 * * * * * | 1 0 2 0 0 | 2 1 0 xo.3xx. ... ...&#x & ♦ 9 | 3 6 6 | 1 1 3 3 0 | * * 192 * * * * | 0 1 1 1 0 | 1 2 0 xo. ... ox. ...&#x & ♦ 4 | 2 0 4 | 0 0 4 0 0 | * * * 72 * * * | 0 2 0 0 2 | 1 2 1 ... xx. ... *b3oo.&#x & ♦ 6 | 0 6 3 | 0 2 0 3 0 | * * * * 96 * * | 0 0 2 1 0 | 1 2 0 xoo ... ... ...&#x & ♦ 4 | 1 0 5 | 0 0 2 0 2 | * * * * * 288 * | 0 0 0 1 2 | 0 2 1 ... xxx ... ...&#x ♦ 6 | 0 3 6 | 0 0 0 3 2 | * * * * * * 96 | 0 0 0 3 0 | 0 3 0 ------------------------+-----+------------+--------------------+------------------------+----------------+-------- x..3x..3o.. *b3o.. & ♦ 48 | 24 96 0 | 32 64 0 0 0 | 16 8 0 0 0 0 0 | 3 * * * * | 2 0 0 xo.3xx.3ox. ...&#x & ♦ 24 | 12 24 24 | 8 8 24 12 0 | 2 0 8 6 0 0 0 | * 24 * * * | 1 1 0 xo.3xx. ... *b3oo.&#x & ♦ 18 | 6 24 12 | 4 12 6 12 0 | 1 1 4 0 4 0 0 | * * 48 * * | 1 1 0 xoo3xxx ... ...&#x & ♦ 12 | 3 9 15 | 1 2 6 9 6 | 0 0 2 0 1 3 3 | * * * 96 * | 0 2 0 xoo ... oxo ...&#x & ♦ 5 | 2 0 8 | 0 0 6 0 4 | 0 0 0 1 0 4 0 | * * * * 144 | 0 1 1 ------------------------+-----+------------+--------------------+------------------------+----------------+-------- xo.3xx.3ox. *b3oo.&#x & ♦ 96 | 48 192 96 | 64 128 96 96 0 | 32 16 64 24 32 0 0 | 2 8 16 0 0 | 3 * * xoo3xxx3oxo ...&#x & ♦ 30 | 12 36 48 | 8 16 36 36 24 | 2 1 16 6 8 24 12 | 0 1 2 8 6 | * 24 * xoo ... oxo oox&#x ♦ 6 | 3 0 12 | 0 0 12 0 8 | 0 0 0 3 0 12 0 | 0 0 0 0 6 | * * 24
x..3x..3o.. *b3o.. || .oo3.xx3.xo *b3.ox&#x → height = sqrt(3/8) = 0.612372 ( thex || gyro (thex || gyro thex) ) o..3o..3o.. *b3o.. | 48 * | 1 4 4 0 0 0 | 4 4 4 8 2 4 0 0 0 0 0 | 4 1 8 2 4 4 4 4 4 0 0 0 0 0 0 | 1 4 4 2 4 4 4 1 0 0 0 | 2 4 1 1 0 .o.3.o.3.o. *b3.o. & | * 96 | 0 0 2 4 1 2 | 0 0 1 4 2 4 2 4 4 4 3 | 0 0 2 1 4 2 2 4 6 2 1 2 2 6 1 | 0 2 1 2 2 3 6 2 1 3 2 | 1 3 1 2 1 ------------------------+-------+---------------------+------------------------------------+----------------------------------------------+-------------------------------+------------ x.. ... ... ... | 2 0 | 24 * * * * * | 4 0 4 0 0 0 0 0 0 0 0 | 4 0 8 2 0 0 4 0 0 0 0 0 0 0 0 | 1 4 4 0 4 4 0 0 0 0 0 | 2 4 1 0 0 ... x.. ... ... | 2 0 | * 96 * * * * | 1 2 0 2 0 0 0 0 0 0 0 | 2 1 2 0 2 2 0 1 0 0 0 0 0 0 0 | 1 2 2 2 1 0 2 0 0 0 0 | 2 2 0 1 0 oo.3oo.3oo. *b3oo.&#x & | 1 1 | * * 192 * * * | 0 0 1 2 1 2 0 0 0 0 0 | 0 0 2 1 2 1 2 2 3 0 0 0 0 0 0 | 0 2 1 1 2 3 3 1 0 0 0 | 1 3 1 1 0 ... .x. ... ... & | 0 2 | * * * 192 * * | 0 0 0 1 0 0 1 1 1 1 0 | 0 0 1 0 1 1 0 1 0 1 1 1 1 2 0 | 0 1 1 1 1 0 2 0 1 2 1 | 1 2 0 1 1 ... ... .x. ... & | 0 2 | * * * * 48 * | 0 0 0 0 2 0 0 4 0 0 2 | 0 0 0 1 4 0 0 0 4 2 0 2 0 4 1 | 0 2 0 2 0 2 4 2 1 2 2 | 1 2 1 2 1 .oo3.oo3.oo *b3.oo&#x | 0 2 | * * * * * 96 | 0 0 0 0 0 2 0 0 0 2 2 | 0 0 0 0 0 0 1 2 4 0 0 0 1 4 1 | 0 0 0 0 1 2 4 2 0 2 2 | 0 2 1 2 1 ------------------------+-------+---------------------+------------------------------------+----------------------------------------------+-------------------------------+------------ x..3x.. ... ... | 6 0 | 3 3 0 0 0 0 | 32 * * * * * * * * * * | 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 | 1 2 2 0 1 0 0 0 0 0 0 | 2 2 0 0 0 ... x..3o.. ... & | 3 0 | 0 3 0 0 0 0 | * 64 * * * * * * * * * | 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 | 1 1 1 2 0 0 1 0 0 0 0 | 2 1 0 1 0 xo. ... ... ...&#x & | 2 1 | 1 0 2 0 0 0 | * * 96 * * * * * * * * | 0 0 2 1 0 0 2 0 0 0 0 0 0 0 0 | 0 2 1 0 2 3 0 0 0 0 0 | 1 3 1 0 0 ... xx. ... ...&#x & | 2 2 | 0 1 2 1 0 0 | * * * 192 * * * * * * * | 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 | 0 1 1 1 1 0 2 0 0 0 0 | 1 2 0 1 0 ... ... ox. ...&#x & | 1 2 | 0 0 2 0 1 0 | * * * * 96 * * * * * * | 0 0 0 1 2 0 0 0 2 0 0 0 0 0 0 | 0 2 0 1 0 2 2 1 0 0 0 | 1 2 1 1 0 ooo3ooo3ooo *b3ooo&#x | 1 2 | 0 0 2 0 0 1 | * * * * * 192 * * * * * | 0 0 0 0 0 0 1 1 2 0 0 0 0 0 0 | 0 0 0 0 1 2 2 1 0 0 0 | 0 2 1 1 0 .o.3.x. ... ... & | 0 3 | 0 0 0 3 0 0 | * * * * * * 64 * * * * | 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 | 0 1 1 0 1 0 0 0 1 2 0 | 1 2 0 0 1 ... .x.3.x. ... & | 0 6 | 0 0 0 3 3 0 | * * * * * * * 64 * * * | 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 | 0 1 0 1 0 0 1 0 1 1 1 | 1 1 0 1 1 ... .x. ... *b3.o. & | 0 3 | 0 0 0 3 0 0 | * * * * * * * * 64 * * | 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 | 0 0 1 1 0 0 1 0 1 1 1 | 1 1 0 1 1 ... .xx ... ...&#x | 0 4 | 0 0 0 2 0 2 | * * * * * * * * * 96 * | 0 0 0 0 0 0 0 1 0 0 0 0 1 2 0 | 0 0 0 0 1 0 2 0 0 2 1 | 0 2 0 1 1 ... ... .xo ...&#x & | 0 3 | 0 0 0 0 1 2 | * * * * * * * * * * 96 | 0 0 0 0 0 0 0 0 2 0 0 0 0 2 1 | 0 0 0 0 0 1 2 2 0 1 2 | 0 1 1 2 1 ------------------------+-------+---------------------+------------------------------------+----------------------------------------------+-------------------------------+------------ x..3x..3o.. ... & ♦ 12 0 | 6 12 0 0 0 0 | 4 4 0 0 0 0 0 0 0 0 0 | 16 * * * * * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 | 2 1 0 0 0 ... x..3o.. *b3o.. ♦ 6 0 | 0 12 0 0 0 0 | 0 8 0 0 0 0 0 0 0 0 0 | * 8 * * * * * * * * * * * * * | 1 0 0 2 0 0 0 0 0 0 0 | 2 0 0 1 0 xo.3xx. ... ...&#x & ♦ 6 3 | 3 3 6 3 0 0 | 1 0 3 3 0 0 1 0 0 0 0 | * * 64 * * * * * * * * * * * * | 0 1 1 0 1 0 0 0 0 0 0 | 1 2 0 0 0 xo. ... ox. ...&#x & ♦ 2 2 | 1 0 4 0 1 0 | 0 0 2 0 2 0 0 0 0 0 0 | * * * 48 * * * * * * * * * * * | 0 2 0 0 0 2 0 0 0 0 0 | 1 2 1 0 0 ... xx.3ox. ...&#x & ♦ 3 6 | 0 3 6 3 3 0 | 0 1 0 3 3 0 0 1 0 0 0 | * * * * 64 * * * * * * * * * * | 0 1 0 1 0 0 1 0 0 0 0 | 1 1 0 1 0 ... xx. ... *b3oo.&#x & ♦ 3 3 | 0 3 3 3 0 0 | 0 1 0 3 0 0 0 0 1 0 0 | * * * * * 64 * * * * * * * * * | 0 0 1 1 0 0 1 0 0 0 0 | 1 1 0 1 0 xoo ... ... ...&#x ♦ 2 2 | 1 0 4 0 0 1 | 0 0 2 0 0 2 0 0 0 0 0 | * * * * * * 96 * * * * * * * * | 0 0 0 0 1 2 0 0 0 0 0 | 0 2 1 0 0 ... xxx ... ...&#x ♦ 2 4 | 0 1 4 2 0 2 | 0 0 0 2 0 2 0 0 0 1 0 | * * * * * * * 96 * * * * * * * | 0 0 0 0 1 0 2 0 0 0 0 | 0 2 0 1 0 ... ... oxo ...&#x & ♦ 1 3 | 0 0 3 0 1 2 | 0 0 0 0 1 2 0 0 0 0 1 | * * * * * * * * 192 * * * * * * | 0 0 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0 .o.3.x.3.x. ... & ♦ 0 12 | 0 0 0 12 6 0 | 0 0 0 0 0 0 4 4 0 0 0 | * * * * * * * * * 16 * * * * * | 0 1 0 0 0 0 0 0 1 1 0 | 1 1 0 0 1 .o.3.x. ... *b3.o. & ♦ 0 6 | 0 0 0 12 0 0 | 0 0 0 0 0 0 4 0 4 0 0 | * * * * * * * * * * 16 * * * * | 0 0 1 0 0 0 0 0 1 1 0 | 1 1 0 0 1 ... .x.3.x. *b3.o. & ♦ 0 12 | 0 0 0 12 6 0 | 0 0 0 0 0 0 0 4 4 0 0 | * * * * * * * * * * * 16 * * * | 0 0 0 1 0 0 0 0 1 0 1 | 1 0 0 1 1 .oo3.xx ... ...&#x ♦ 0 6 | 0 0 0 6 0 3 | 0 0 0 0 0 0 2 0 0 3 0 | * * * * * * * * * * * * 32 * * | 0 0 0 0 1 0 0 0 0 2 0 | 0 2 0 0 1 ... .xx3.xo ...&#x & ♦ 0 9 | 0 0 0 6 3 6 | 0 0 0 0 0 0 0 1 1 3 3 | * * * * * * * * * * * * * 64 * | 0 0 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1 ... ... .xo .ox&#x ♦ 0 4 | 0 0 0 0 2 4 | 0 0 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * * * * 24 | 0 0 0 0 0 0 0 2 0 0 2 | 0 0 1 2 1 ------------------------+-------+---------------------+------------------------------------+----------------------------------------------+-------------------------------+------------ x..3x..3o.. *b3o.. ♦ 48 0 | 24 96 0 0 0 0 | 32 64 0 0 0 0 0 0 0 0 0 | 16 8 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * | 2 0 0 0 0 xo.3xx.3ox. ...&#x & ♦ 12 12 | 6 12 24 12 6 0 | 4 4 12 12 12 0 4 4 0 0 0 | 1 0 4 6 4 0 0 0 0 1 0 0 0 0 0 | * 16 * * * * * * * * * | 1 1 0 0 0 xo.3xx. ... *b3oo.&#x & ♦ 12 6 | 6 12 12 12 0 0 | 4 4 6 12 0 0 4 0 4 0 0 | 1 0 4 0 0 4 0 0 0 0 1 0 0 0 0 | * * 16 * * * * * * * * | 1 1 0 0 0 ... xx.3ox. *b3oo.&#x & ♦ 6 12 | 0 12 12 12 6 0 | 0 8 0 12 6 0 0 4 4 0 0 | 0 1 0 0 4 4 0 0 0 0 0 1 0 0 0 | * * * 16 * * * * * * * | 1 0 0 1 0 xoo3xxx ... ...&#x ♦ 6 6 | 3 3 12 6 0 3 | 1 0 6 6 0 6 2 0 0 3 0 | 0 0 2 0 0 0 3 3 0 0 0 0 1 0 0 | * * * * 32 * * * * * * | 0 2 0 0 0 xoo ... oxo ...&#x & ♦ 2 3 | 1 0 6 0 1 2 | 0 0 3 0 2 4 0 0 0 0 1 | 0 0 0 1 0 0 2 0 2 0 0 0 0 0 0 | * * * * * 96 * * * * * | 0 1 1 0 0 ... xxx3oxo ...&#x & ♦ 3 9 | 0 3 9 6 3 6 | 0 1 0 6 3 6 0 1 1 3 3 | 0 0 0 0 1 1 0 3 3 0 0 0 0 1 0 | * * * * * * 64 * * * * | 0 1 0 1 0 ... ... oxo oox&#x ♦ 1 4 | 0 0 4 0 2 4 | 0 0 0 0 2 4 0 0 0 0 4 | 0 0 0 0 0 0 0 0 4 0 0 0 0 0 1 | * * * * * * * 48 * * * | 0 0 1 1 0 .o.3.x.3.x. *b3.o. & ♦ 0 48 | 0 0 0 96 24 0 | 0 0 0 0 0 0 32 32 32 0 0 | 0 0 0 0 0 0 0 0 0 8 8 8 0 0 0 | * * * * * * * * 2 * * | 1 0 0 0 1 .oo3.xx3.xo ...&#x & ♦ 0 18 | 0 0 0 24 6 12 | 0 0 0 0 0 0 8 4 4 12 6 | 0 0 0 0 0 0 0 0 0 1 1 0 4 4 0 | * * * * * * * * * 16 * | 0 1 0 0 1 ... .xx3.xo *b3.ox&#x ♦ 0 24 | 0 0 0 24 12 24 | 0 0 0 0 0 0 0 8 8 12 24 | 0 0 0 0 0 0 0 0 0 0 0 2 0 8 6 | * * * * * * * * * * 8 | 0 0 0 1 1 ------------------------+-------+---------------------+------------------------------------+----------------------------------------------+-------------------------------+------------ xo.3xx.3ox. *b3oo.&#x & ♦ 48 48 | 24 96 96 96 24 0 | 32 64 48 96 48 0 32 32 32 0 0 | 16 8 32 24 32 32 0 0 0 8 8 8 0 0 0 | 1 8 8 8 0 0 0 0 1 0 0 | 2 * * * * xoo3xxx3oxo ...&#x & ♦ 12 18 | 6 12 36 24 6 12 | 4 4 18 24 12 24 8 4 4 12 6 | 1 0 8 6 4 4 12 12 12 1 1 0 4 4 0 | 0 1 1 0 4 6 4 0 0 1 0 | * 16 * * * xoo ... oxo oox&#x ♦ 2 4 | 1 0 8 0 2 4 | 0 0 4 0 4 8 0 0 0 0 4 | 0 0 0 2 0 0 4 0 8 0 0 0 0 0 1 | 0 0 0 0 0 4 0 2 0 0 0 | * * 24 * * ... xxx3oxo *b3oox&#x ♦ 6 24 | 0 12 24 24 12 24 | 0 8 0 24 12 24 0 8 8 12 24 | 0 1 0 0 8 8 0 12 24 0 0 2 0 8 6 | 0 0 0 2 0 0 8 6 0 0 1 | * * * 8 * .oo3.xx3.xo *b3.ox&#x ♦ 0 96 | 0 0 0 192 48 96 | 0 0 0 0 0 0 64 64 64 96 96 | 0 0 0 0 0 0 0 0 0 16 16 16 32 64 24 | 0 0 0 0 0 0 0 0 2 16 8 | * * * * 1
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