Acronym | ritgyt |
Name | rectified-tesseractic gyrotrigonism |
Circumradius | sqrt(5/3) = 1.290994 |
Lace city in approx. ASCII-art |
where: E E = x3o3x *b3o (rit) X O = x3o3o *b3x O X = o3o3x *b3x |
Face vector | 96, 576, 1224, 1080, 387, 51 |
Confer |
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By means of a (partial) Stott expansion at the central node positions, applied simultanuously to all layers, this polypeton would produce tahgyt.
This polypeton also can be obtained from rojak by chopping off cyclically 3 rats down to their (then intersecting) siphin sefas. In fact, each rit is just the medial segment of those siphins.
Incidence matrix according to Dynkin symbol
xxo3ooo3xox *b3oxx&#x → all pairwise heights = 1/sqrt(2) = 0.707107 o..3o..3o.. *b3o.. & | 96 | 6 6 | 6 3 12 18 3 | 3 2 6 18 8 6 15 | 1 8 6 2 7 12 | 2 5 3 ------------------------+----+---------+-------------------+--------------------------+-------------------+-------- x.. ... ... ... & | 2 | 288 * | 2 1 2 2 0 | 2 1 2 5 2 1 2 | 1 5 2 1 2 3 | 2 3 1 oo.3oo.3oo. *b3oo.&#x & | 2 | * 288 | 0 0 2 4 1 | 0 0 1 4 2 2 6 | 0 2 2 1 3 6 | 1 3 2 ------------------------+----+---------+-------------------+--------------------------+-------------------+-------- x..3o.. ... ... & | 3 | 3 0 | 192 * * * * | 1 1 1 0 1 0 0 | 1 3 0 1 1 0 | 2 2 0 x.. ... x.. ... & | 4 | 4 0 | * 72 * * * | 2 0 0 4 0 0 0 | 1 4 2 0 0 2 | 2 2 1 xx. ... ... ...&#x & | 4 | 2 2 | * * 288 * * | 0 0 1 2 0 0 1 | 0 2 1 0 1 2 | 1 2 1 ... ... xo. ...&#x & | 3 | 1 2 | * * * 576 * | 0 0 0 1 1 1 1 | 0 1 1 1 1 2 | 1 2 1 ooo3ooo3ooo *b3ooo&#x | 3 | 0 3 | * * * * 96 | 0 0 0 0 0 0 6 | 0 0 0 0 3 6 | 0 3 2 ------------------------+----+---------+-------------------+--------------------------+-------------------+-------- x..3o..3x.. ... & ♦ 12 | 24 0 | 8 6 0 0 0 | 24 * * * * * * | 1 2 0 0 0 0 | 2 1 0 x..3o.. ... *b3o.. & ♦ 4 | 6 0 | 4 0 0 0 0 | * 48 * * * * * | 1 1 0 1 0 0 | 2 1 0 xx.3oo. ... ...&#x & ♦ 6 | 6 3 | 2 0 3 0 0 | * * 96 * * * * | 0 2 0 0 1 0 | 1 2 0 xx. ... xo. ...&#x & ♦ 6 | 5 4 | 0 1 2 2 0 | * * * 288 * * * | 0 1 1 0 0 1 | 1 1 1 ... oo.3xo. ...&#x & ♦ 4 | 3 3 | 1 0 0 3 0 | * * * * 192 * * | 0 1 0 1 1 0 | 1 2 0 ... ... xo. ox.&#x & ♦ 4 | 2 4 | 0 0 0 4 0 | * * * * * 144 * | 0 0 1 1 0 1 | 1 1 1 xxo ... ... ...&#x & ♦ 5 | 2 6 | 0 0 1 2 2 | * * * * * * 288 | 0 0 0 0 1 2 | 0 2 1 ------------------------+----+---------+-------------------+--------------------------+-------------------+-------- x..3o..3x.. *b3o.. & ♦ 32 | 96 0 | 64 24 0 0 0 | 8 16 0 0 0 0 0 | 3 * * * * * | 2 0 0 xx.3oo.3xo. ...&#x & ♦ 16 | 30 12 | 12 6 12 12 0 | 1 1 4 6 4 0 0 | * 48 * * * * | 1 1 0 xx. ... xo. ox.&#x & ♦ 8 | 8 8 | 0 2 4 8 0 | 0 0 0 4 0 2 0 | * * 72 * * * | 1 0 1 ... oo.3xo. *b3ox.&#x & ♦ 8 | 12 12 | 8 0 0 24 0 | 0 2 0 0 8 6 0 | * * * 24 * * | 1 1 0 xxo3ooo ... ...&#x & ♦ 7 | 6 9 | 2 0 3 6 3 | 0 0 1 0 2 0 3 | * * * * 96 * | 0 2 0 xxo ... xox ...&#x & ♦ 8 | 6 12 | 0 1 4 8 4 | 0 0 0 2 0 1 4 | * * * * * 144 | 0 1 1 ------------------------+----+---------+-------------------+--------------------------+-------------------+-------- xx.3oo.3xo. *b3ox.&#x & ♦ 64 | 192 96 | 128 48 96 192 0 | 16 32 32 96 64 48 0 | 2 16 24 8 0 0 | 3 * * xxo3ooo3xox ...&#x & ♦ 20 | 36 36 | 16 6 24 48 12 | 1 2 8 12 16 6 24 | 0 2 0 1 8 6 | * 24 * xxo ... xox oxx&#x ♦ 12 | 12 24 | 0 3 12 24 8 | 0 0 0 12 0 6 12 | 0 0 3 0 0 6 | * * 24
x..3o..3x.. *b3o.. || .xo3.oo3.ox *b3.xx&#x → height = sqrt(3/8) = 0.612372 ( rit || gyro (rit || gyro rit) ) o..3o..3o.. *b3o.. | 32 * | 6 6 0 0 0 | 6 3 12 12 6 3 0 0 0 0 0 | 3 2 6 12 6 6 2 6 12 3 0 0 0 0 0 0 0 | 1 6 2 6 2 6 6 6 1 0 0 0 0 | 2 3 2 3 0 .o.3.o.3.o. *b3.o. & | * 64 | 0 3 3 3 3 | 0 0 6 3 6 3 3 3 3 9 6 | 0 0 3 3 6 1 3 3 9 6 1 3 1 4 3 9 3 | 0 1 3 3 1 4 3 9 3 1 1 3 4 | 1 1 4 3 1 ------------------------+-------+-----------------+--------------------------------------+----------------------------------------------------+-------------------------------------+------------ x.. ... ... ... & | 2 0 | 96 * * * * | 2 1 2 2 0 0 0 0 0 0 0 | 2 1 2 4 1 2 0 1 2 0 0 0 0 0 0 0 0 | 1 4 1 2 1 2 2 1 0 0 0 0 0 | 2 2 1 1 0 oo.3oo.3oo. *b3oo.&#x & | 1 1 | * 192 * * * | 0 0 2 2 2 1 0 0 0 0 0 | 0 0 1 2 2 1 1 2 4 2 0 0 0 0 0 0 0 | 0 1 1 2 1 2 2 4 1 0 0 0 0 | 1 1 2 2 0 .x. ... ... ... & | 0 2 | * * 96 * * | 0 0 2 0 0 0 2 1 0 2 0 | 0 0 2 1 2 0 0 0 2 0 1 2 0 2 1 2 0 | 0 1 2 1 0 2 1 2 0 1 1 1 2 | 1 1 2 1 1 ... ... ... .x. & | 0 2 | * * * 96 * | 0 0 0 0 2 0 0 1 2 0 2 | 0 0 0 0 2 0 2 1 0 2 0 2 1 0 0 3 2 | 0 0 2 1 1 0 0 3 2 1 0 1 3 | 1 0 3 1 1 .oo3.oo3.oo *b3.oo&#x | 0 2 | * * * * 96 | 0 0 0 0 0 1 0 0 0 4 2 | 0 0 0 0 0 0 0 0 4 2 0 0 0 2 2 4 1 | 0 0 0 0 0 2 2 4 1 0 1 2 2 | 0 1 2 2 1 ------------------------+-------+-----------------+--------------------------------------+----------------------------------------------------+-------------------------------------+------------ x..3o.. ... ... & | 3 0 | 3 0 0 0 0 | 64 * * * * * * * * * * | 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | 1 2 1 0 1 1 0 0 0 0 0 0 0 | 2 1 1 0 0 x.. ... x.. ... | 4 0 | 4 0 0 0 0 | * 24 * * * * * * * * * | 2 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 4 0 2 0 0 2 0 0 0 0 0 0 | 2 2 0 1 0 xx. ... ... ...&#x & | 2 2 | 1 2 1 0 0 | * * 192 * * * * * * * * | 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 | 0 1 1 1 0 1 1 1 0 0 0 0 0 | 1 1 1 1 0 ... ... xo. ...&#x & | 2 1 | 1 2 0 0 0 | * * * 192 * * * * * * * | 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 | 0 1 0 1 1 1 1 1 0 0 0 0 0 | 1 1 1 1 0 ... ... ... ox.&#x & | 1 2 | 0 2 0 1 0 | * * * * 192 * * * * * * | 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 | 0 0 1 1 1 0 0 2 1 0 0 0 0 | 1 0 2 1 0 ooo3ooo3ooo *b3ooo&#x | 1 2 | 0 2 0 0 1 | * * * * * 96 * * * * * | 0 0 0 0 0 0 0 0 4 2 0 0 0 0 0 0 0 | 0 0 0 0 0 2 2 4 1 0 0 0 0 | 0 1 2 2 0 .x.3.o. ... ... & | 0 3 | 0 0 3 0 0 | * * * * * * 64 * * * * | 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 | 0 1 1 0 0 1 0 0 0 1 1 0 1 | 1 1 1 0 1 .x. ... ... .x. & | 0 4 | 0 0 2 2 0 | * * * * * * * 48 * * * | 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 2 0 | 0 0 2 1 0 0 0 2 0 1 0 1 2 | 1 0 2 1 1 ... .o. ... *b3.x. & | 0 3 | 0 0 0 3 0 | * * * * * * * * 64 * * | 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 | 0 0 1 0 1 0 0 0 1 1 0 0 2 | 1 0 2 0 1 .xo ... ... ...&#x & | 0 3 | 0 0 1 0 2 | * * * * * * * * * 192 * | 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 | 0 0 0 0 0 1 1 1 0 0 1 1 1 | 0 1 1 1 1 ... ... ... .xx | 0 4 | 0 0 0 2 2 | * * * * * * * * * * 96 | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 2 1 | 0 0 0 0 0 0 0 2 1 0 0 1 2 | 0 0 2 1 1 ------------------------+-------+-----------------+--------------------------------------+----------------------------------------------------+-------------------------------------+------------ x..3o..3x.. ... ♦ 12 0 | 24 0 0 0 0 | 8 6 0 0 0 0 0 0 0 0 0 | 8 * * * * * * * * * * * * * * * * | 1 2 0 0 0 0 0 0 0 0 0 0 0 | 2 1 0 0 0 x..3o.. ... *b3o.. & ♦ 4 0 | 6 0 0 0 0 | 4 0 0 0 0 0 0 0 0 0 0 | * 16 * * * * * * * * * * * * * * * | 1 0 1 0 1 0 0 0 0 0 0 0 0 | 2 0 1 0 0 xx.3oo. ... ...&#x & ♦ 3 3 | 3 3 3 0 0 | 1 0 3 0 0 0 1 0 0 0 0 | * * 64 * * * * * * * * * * * * * * | 0 1 1 0 0 1 0 0 0 0 0 0 0 | 1 1 1 0 0 xx. ... xo. ...&#x & ♦ 4 2 | 4 4 1 0 0 | 0 1 2 2 0 0 0 0 0 0 0 | * * * 96 * * * * * * * * * * * * * | 0 1 0 1 0 0 1 0 0 0 0 0 0 | 1 1 0 1 0 xx. ... ... ox.&#x & ♦ 2 4 | 1 4 2 2 0 | 0 0 2 0 2 0 0 1 0 0 0 | * * * * 96 * * * * * * * * * * * * | 0 0 1 1 0 0 0 1 0 0 0 0 0 | 1 0 1 1 0 ... oo.3xo. ...&#x & ♦ 3 1 | 3 3 0 0 0 | 1 0 0 3 0 0 0 0 0 0 0 | * * * * * 64 * * * * * * * * * * * | 0 1 0 0 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 ... oo. ... *b3ox.&#x & ♦ 1 3 | 0 3 0 3 0 | 0 0 0 0 3 0 0 0 1 0 0 | * * * * * * 64 * * * * * * * * * * | 0 0 1 0 1 0 0 0 1 0 0 0 0 | 1 0 2 0 0 ... ... xo. ox.&#x & ♦ 2 2 | 1 4 0 1 0 | 0 0 0 2 2 0 0 0 0 0 0 | * * * * * * * 96 * * * * * * * * * | 0 0 0 1 1 0 0 1 0 0 0 0 0 | 1 0 1 1 0 xxo ... ... ...&#x & ♦ 2 3 | 1 4 1 0 2 | 0 0 1 1 0 2 0 0 0 1 0 | * * * * * * * * 192 * * * * * * * * | 0 0 0 0 0 1 1 1 0 0 0 0 0 | 0 1 1 1 0 ... ... ... oxx&#x ♦ 1 4 | 0 4 0 2 2 | 0 0 0 0 2 2 0 0 0 0 1 | * * * * * * * * * 96 * * * * * * * | 0 0 0 0 0 0 0 2 1 0 0 0 0 | 0 0 2 1 0 .x.3.o.3.o. ... & ♦ 0 4 | 0 0 6 0 0 | 0 0 0 0 0 0 4 0 0 0 0 | * * * * * * * * * * 16 * * * * * * | 0 1 0 0 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1 .x.3.o. ... *b3.x. & ♦ 0 12 | 0 0 12 12 0 | 0 0 0 0 0 0 4 6 4 0 0 | * * * * * * * * * * * 16 * * * * * | 0 0 1 0 0 0 0 0 0 1 0 0 1 | 1 0 1 0 1 ... .o.3.o. *b3.x. & ♦ 0 4 | 0 0 0 6 0 | 0 0 0 0 0 0 0 0 4 0 0 | * * * * * * * * * * * * 16 * * * * | 0 0 0 0 1 0 0 0 0 1 0 0 1 | 1 0 1 0 1 .xo3.oo ... ...&#x & ♦ 0 4 | 0 0 3 0 3 | 0 0 0 0 0 0 1 0 0 3 0 | * * * * * * * * * * * * * 64 * * * | 0 0 0 0 0 1 0 0 0 0 1 0 1 | 0 1 1 0 1 .xo ... .ox ...&#x ♦ 0 4 | 0 0 2 0 4 | 0 0 0 0 0 0 0 0 0 4 0 | * * * * * * * * * * * * * * 48 * * | 0 0 0 0 0 0 1 0 0 0 1 1 0 | 0 1 0 1 1 .xo ... ... .xx&#x & ♦ 0 6 | 0 0 2 3 4 | 0 0 0 0 0 0 0 1 0 2 2 | * * * * * * * * * * * * * * * 96 * | 0 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 1 1 1 ... .oo ... *b3.xx&#x ♦ 0 6 | 0 0 0 6 3 | 0 0 0 0 0 0 0 0 2 0 3 | * * * * * * * * * * * * * * * * 32 | 0 0 0 0 0 0 0 0 1 0 0 0 2 | 0 0 2 0 1 ------------------------+-------+-----------------+--------------------------------------+----------------------------------------------------+-------------------------------------+------------ x..3o..3x.. *b3o.. ♦ 32 0 | 96 0 0 0 0 | 64 24 0 0 0 0 0 0 0 0 0 | 8 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * | 2 0 0 0 0 xx.3oo.3xo. ...&#x & ♦ 12 4 | 24 12 6 0 0 | 8 6 12 12 0 0 4 0 0 0 0 | 1 0 4 6 0 4 0 0 0 0 1 0 0 0 0 0 0 | * 16 * * * * * * * * * * * | 1 1 0 0 0 xx.3oo. ... *b3ox.&#x & ♦ 4 12 | 6 12 12 12 0 | 4 0 12 0 12 0 4 6 4 0 0 | 0 1 4 0 6 0 4 0 0 0 0 1 0 0 0 0 0 | * * 16 * * * * * * * * * * | 1 0 1 0 0 xx. ... xo. ox.&#x & ♦ 4 4 | 4 8 2 2 0 | 0 1 4 4 4 0 0 1 0 0 0 | 0 0 0 2 2 0 0 2 0 0 0 0 0 0 0 0 0 | * * * 48 * * * * * * * * * | 1 0 0 1 0 ... oo.3xo. *b3ox.&#x & ♦ 4 4 | 6 12 0 6 0 | 4 0 0 12 12 0 0 0 4 0 0 | 0 1 0 0 0 4 4 6 0 0 0 0 1 0 0 0 0 | * * * * 16 * * * * * * * * | 1 0 1 0 0 xxo3ooo ... ...&#x & ♦ 3 4 | 3 6 3 0 3 | 1 0 3 3 0 3 1 0 0 3 0 | 0 0 1 0 0 1 0 0 3 0 0 0 0 1 0 0 0 | * * * * * 64 * * * * * * * | 0 1 1 0 0 xxo ... xox ...&#x ♦ 4 4 | 4 8 2 0 4 | 0 1 4 4 0 4 0 0 0 4 0 | 0 0 0 2 0 0 0 0 4 0 0 0 0 0 1 0 0 | * * * * * * 48 * * * * * * | 0 1 0 1 0 xxo ... ... oxx&#x & ♦ 2 6 | 1 8 2 3 4 | 0 0 2 2 4 4 0 1 0 2 2 | 0 0 0 0 1 0 0 1 2 2 0 0 0 0 0 1 0 | * * * * * * * 96 * * * * * | 0 0 1 1 0 ... ooo ... *b3oxx&#x ♦ 1 6 | 0 6 0 6 3 | 0 0 0 0 6 3 0 0 2 0 3 | 0 0 0 0 0 0 2 0 0 3 0 0 0 0 0 0 1 | * * * * * * * * 32 * * * * | 0 0 2 0 0 .x.3.o.3.o. *b3.x. & ♦ 0 32 | 0 0 48 48 0 | 0 0 0 0 0 0 32 24 32 0 0 | 0 0 0 0 0 0 0 0 0 0 8 8 8 0 0 0 0 | * * * * * * * * * 2 * * * | 1 0 0 0 1 .xo3.oo3.ox ...&#x ♦ 0 8 | 0 0 12 0 12 | 0 0 0 0 0 0 8 0 0 24 0 | 0 0 0 0 0 0 0 0 0 0 2 0 0 8 6 0 0 | * * * * * * * * * * 8 * * | 0 1 0 0 1 .xo ... .ox .xx&#x ♦ 0 8 | 0 0 4 4 8 | 0 0 0 0 0 0 0 2 0 8 4 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 0 | * * * * * * * * * * * 24 * | 0 0 0 1 1 ... .oo3.ox *b3.xx&#x & ♦ 0 16 | 0 0 12 18 12 | 0 0 0 0 0 0 4 6 8 12 12 | 0 0 0 0 0 0 0 0 0 0 0 1 1 4 0 6 4 | * * * * * * * * * * * * 16 | 0 0 1 0 1 ------------------------+-------+-----------------+--------------------------------------+----------------------------------------------------+-------------------------------------+------------ xx.3oo.3xo. *b3ox.&#x & ♦ 32 32 | 96 96 48 48 0 | 64 24 96 96 96 0 32 24 32 0 0 | 8 16 32 48 48 32 32 48 0 0 8 8 8 0 0 0 0 | 1 8 8 24 8 0 0 0 0 1 0 0 0 | 2 * * * * xxo3ooo3xox ...&#x ♦ 12 8 | 24 24 12 0 12 | 8 6 24 24 0 12 8 0 0 24 0 | 1 0 8 12 0 8 0 0 24 0 2 0 0 8 6 0 0 | 0 2 0 0 0 8 6 0 0 0 1 0 0 | * 8 * * * xxo3ooo ... *b3oxx&#x & ♦ 4 16 | 6 24 12 18 12 | 4 0 12 12 24 12 4 6 8 12 12 | 0 1 4 0 6 4 8 6 12 12 0 1 1 4 0 6 4 | 0 0 1 0 1 4 0 6 4 0 0 0 1 | * * 16 * * xxo ... xox oxx&#x ♦ 4 8 | 4 16 4 4 8 | 0 1 8 8 8 8 0 2 0 8 4 | 0 0 0 4 4 0 0 4 8 4 0 0 0 0 2 4 0 | 0 0 0 2 0 0 2 4 0 0 0 1 0 | * * * 24 * .xo3.oo3.ox *b3.xx&#x ♦ 0 64 | 0 0 96 96 96 | 0 0 0 0 0 0 64 48 64 192 96 | 0 0 0 0 0 0 0 0 0 0 16 16 16 64 45 96 32 | 0 0 0 0 0 0 0 0 0 2 8 24 16 | * * * * 1
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