cytau tes

Acronym	cytau tes
Name	cyclotetraaugmented tesseract, cyclotetradiminished icositetrachoron
Circumradius	1
Lace city in approx. ASCII-art	x4o x4o o4q x4o x4o
Lace city in approx. ASCII-art	o4o x4o o4o x4o x4o o4o x4o o4o
Dihedral angles	at {4} between cube and squippy: 135° at {3} between oct and squippy: 120° at {3} between squippy and squippy: 120° at {4} between cube and cube: 90°
Face vector	20, 64, 68, 24
Confer	uniform relative: ico tes segmentochora: cubpy {4} \|\| co related CRFs: ecubedpy general polytopal classes: bistratic lace towers

This CRF polychoron can be obtained by augmenting a cycle of 4 cubes of tes with cubpies. Note, that neighbouring squippies then reconnect to octs.

It likewise can be obtained from ico by diminishing a cycle of 4 vertices.

Furthermore it is obtainable as the blend of 2 {4} || coes, belnded at the common co, but having the squares orthogonally aligned, i.e. as different diagonals of an encasing oct.

Incidence matrix according to Dynkin symbol

ox4qo ox4oo&#zx   → all heights = 0
(tegum sum of q-{4} and gyro tes)

o.4o. o.4o.     | 4  * ♦  8  0  0 |  4  8 0  0 |  4 2 0  (tips)
.o4.o .o4.o     | * 16 |  2  2  2 |  2  4 1  4 |  4 1 2  (base tes)
----------------+------+----------+------------+-------
oo4oo oo4oo&#x  | 1  1 | 32  *  * |  1  2 0  0 |  2 1 0
.x .. .. ..     | 0  2 |  * 16  * |  1  0 1  2 |  2 0 2
.. .. .x ..     | 0  2 |  *  * 16 |  0  2 0  2 |  2 1 1
----------------+------+----------+------------+-------
ox .. .. ..     | 1  2 |  2  1  0 | 16  * *  * |  2 0 0
.. .. ox ..     | 1  2 |  2  0  1 |  * 32 *  * |  1 1 0
.x4.o .. ..     | 0  4 |  0  4  0 |  *  * 4  * |  0 0 2
.x .. .x ..     | 0  4 |  0  2  2 |  *  * * 16 |  1 0 1
----------------+------+----------+------------+-------
ox .. ox ..&#x  ♦ 1  4 |  4  2  2 |  2  2 0  1 | 16 * *
.. qo ox4oo&#zx ♦ 2  4 |  8  0  4 |  0  8 0  0 |  * 4 *
.x4.o .x ..     ♦ 0  8 |  0  8  4 |  0  0 2  4 |  * * 4

qoo ooq xox4oqo&#zx   → height = 0
(tegum sum of q-{4} with 2 gyrated, lacing-ortho (x,x,q)-cubes)

o.. o.. o..4o..     & | 16 * |  2  2  2 | 1  2  4  4 | 2 1  4
.o. .o. .o.4.o.       |  * 4 ♦  0  8  0 | 0  4  0  8 | 0 2  4
----------------------+------+----------+------------+-------
... ... x.. ...     & |  2 0 | 16  *  * | 1  1  2  0 | 2 0  2
oo. oo. oo.4oo.&#x  & |  1 1 |  * 32  * | 0  1  0  2 | 0 1  2
o.o o.o o.o4o.o&#x    |  2 0 |  *  * 16 | 0  0  2  2 | 1 1  2
----------------------+------+----------+------------+-------
... ... x..4o..     & |  4 0 |  4  0  0 | 4  *  *  * | 2 0  0
... ... xo. ...&#x  & |  2 1 |  1  2  0 | * 16  *  * | 0 0  2
... ... x.x ...&#x    |  4 0 |  2  0  2 | *  * 16  * | 1 0  1
ooo ooo ooo4ooo&#x    |  2 1 |  0  2  1 | *  *  * 32 | 0 1  1
----------------------+------+----------+------------+-------
... ... x.x4o.o&#x    ♦  8 0 |  8  0  4 | 2  0  4  0 | 4 *  *
qoo ooq ... oqo&#zx   ♦  4 2 |  0  8  4 | 0  0  0  8 | * 4  *
... ... xox ...&#x    ♦  4 1 |  2  4  2 | 0  2  1  2 | * * 16

xox xox4oqo&#xt   → both heights = 1/2
(cube || pseudo gyro q-{4} || cube)

o.. o..4o..     | 8 * * | 1 2  2 1  0 0 0 | 2 1 2 2 2  2 0 0 0 0 | 1 2 1 1 2 0 0
.o. .o.4.o.     | * 4 * ♦ 0 0  4 0  4 0 0 | 0 0 2 2 0  4 2 2 0 0 | 0 1 0 2 2 1 0
..o ..o4..o     | * * 8 | 0 0  0 1  2 1 2 | 0 0 0 0 2  2 2 2 2 1 | 0 0 1 1 2 2 1
----------------+-------+-----------------+----------------------+--------------
x.. ... ...     | 2 0 0 | 4 *  * *  * * * | 2 0 2 0 0  0 0 0 0 0 | 1 2 0 1 0 0 0
... x.. ...     | 2 0 0 | * 8  * *  * * * | 1 1 0 1 1  0 0 0 0 0 | 1 1 1 0 1 0 0
oo. oo.4oo.&#x  | 1 1 0 | * * 16 *  * * * | 0 0 1 1 0  1 0 0 0 0 | 0 1 0 1 1 0 0
o.o o.o4o.o&#x  | 1 0 1 | * *  * 8  * * * | 0 0 0 0 2  2 0 0 0 0 | 0 0 1 1 2 0 0
.oo .oo4.oo&#x  | 0 1 1 | * *  * * 16 * * | 0 0 0 0 0  1 1 1 0 0 | 0 0 0 1 1 1 0
..x ... ...     | 0 0 2 | * *  * *  * 4 * | 0 0 0 0 0  0 2 0 2 0 | 0 0 0 1 0 2 1
... ..x ...     | 0 0 2 | * *  * *  * * 8 | 0 0 0 0 1  0 0 1 1 1 | 0 0 1 0 1 1 1
----------------+-------+-----------------+----------------------+--------------
x.. x.. ...     | 4 0 0 | 2 2  0 0  0 0 0 | 4 * * * *  * * * * * | 1 1 0 0 0 0 0
... x..4o..     | 4 0 0 | 0 4  0 0  0 0 0 | * 2 * * *  * * * * * | 1 0 1 0 0 0 0
xo. ... ...&#x  | 2 1 0 | 1 0  2 0  0 0 0 | * * 8 * *  * * * * * | 0 1 0 1 0 0 0
... xo. ...&#x  | 2 1 0 | 0 1  2 0  0 0 0 | * * * 8 *  * * * * * | 0 1 0 0 1 0 0
... x.x ...&#x  | 2 0 2 | 0 1  0 2  0 0 1 | * * * * 8  * * * * * | 0 0 1 0 1 0 0
ooo ooo4ooo&#x  | 1 1 1 | 0 0  1 1  1 0 0 | * * * * * 16 * * * * | 0 0 0 1 1 0 0
.ox ... ...&#x  | 0 1 2 | 0 0  0 0  2 1 0 | * * * * *  * 8 * * * | 0 0 0 1 0 1 0
... .ox ...&#x  | 0 1 2 | 0 0  0 0  2 0 1 | * * * * *  * * 8 * * | 0 0 0 0 1 1 0
..x ..x ...     | 0 0 4 | 0 0  0 0  0 2 2 | * * * * *  * * * 4 * | 0 0 0 0 0 1 1
... ..x4..o     | 0 0 4 | 0 0  0 0  0 0 4 | * * * * *  * * * * 2 | 0 0 1 0 0 0 1
----------------+-------+-----------------+----------------------+--------------
x.. x..4o..     ♦ 8 0 0 | 4 8  0 0  0 0 0 | 4 2 0 0 0  0 0 0 0 0 | 1 * * * * * *
xo. xo. ...&#x  ♦ 4 1 0 | 2 2  4 0  0 0 0 | 1 0 2 2 0  0 0 0 0 0 | * 4 * * * * *
... x.x4o.o&#x  ♦ 4 0 4 | 0 4  0 4  0 0 4 | 0 1 0 0 4  0 0 0 0 1 | * * 2 * * * *
xox ... oqo&#xt ♦ 2 2 2 | 1 0  4 2  4 1 0 | 0 0 2 0 0  4 2 0 0 0 | * * * 4 * * *
... xox ...&#x  ♦ 2 1 2 | 0 1  2 2  2 0 1 | 0 0 0 1 1  2 0 1 0 0 | * * * * 8 * *
.ox .ox ...&#x  ♦ 0 1 4 | 0 0  0 0  4 2 2 | 0 0 0 0 0  0 2 2 1 0 | * * * * * 4 *
..x ..x4..o     ♦ 0 0 8 | 0 0  0 0  0 4 8 | 0 0 0 0 0  0 0 0 4 2 | * * * * * * 1

(qo)q(qo) (oo)o(oo)4(ox)x(ox)&#xt   → both heights 1/sqrt(2) = 0.707107
(oct || pseudo (q,x)-cube || oct)

(o.).(..) (o.).(..)4(o.).(..)     & | 4 * * |  4  4 0  0 0 |  4  4  4  0 0 | 1  4 1 0
(.o).(..) (.o).(..)4(.o).(..)     & | * 8 * |  2  0 2  2 0 |  4  0  2  4 1 | 1  4 0 2
(..)o(..) (..)o(..)4(..)o(..)       | * * 8 |  0  2 0  2 2 |  0  4  2  4 1 | 0  4 1 2
------------------------------------+-------+--------------+---------------+---------
(oo).(..) (oo).(..)4(oo).(..)&#x  & | 1 1 0 | 16  * *  * * |  2  0  1  0 0 | 1  2 0 0
(o.)o(..) (o.)o(..)4(o.)o(..)&#x  & | 1 0 1 |  * 16 *  * * |  0  2  1  0 0 | 0  2 1 0
(..).(..) (..).(..) (.x).(..)     & | 0 2 0 |  *  * 8  * * |  2  0  0  2 0 | 1  2 0 1
(.o)o(..) (.o)o(..)4(.o)o(..)&#x  & | 0 1 1 |  *  * * 16 * |  0  0  1  2 1 | 0  2 0 2
(..).(..) (..).(..) (..)x(..)       | 0 0 2 |  *  * *  * 8 |  0  2  0  2 0 | 0  2 1 1
------------------------------------+-------+--------------+---------------+---------
(..).(..) (..).(..) (ox).(..)&#x  & | 1 2 0 |  2  0 1  0 0 | 16  *  *  * * | 1  1 0 0
(..).(..) (..).(..) (o.)x(..)&#x  & | 1 0 2 |  0  2 0  0 1 |  * 16  *  * * | 0  1 1 0
(oo)o(..) (oo)o(..)4(oo)o(..)&#x  & | 1 1 1 |  1  1 0  1 0 |  *  * 16  * * | 0  2 0 0
(..).(..) (..).(..) (.x)x(..)&#x  & | 0 2 2 |  0  0 1  2 1 |  *  *  * 16 * | 0  1 0 1
(.o)q(.o) (..).(..) (..).(..)&#xt   | 0 2 2 |  0  0 0  4 0 |  *  *  *  * 4 | 0  0 0 2
------------------------------------+-------+--------------+---------------+---------
(qo).(..) (oo).(..)4(ox).(..)&#x  & ♦ 2 4 0 |  8  0 4  0 0 |  8  0  0  0 0 | 2  * * *
(..).(..) (..).(..) (ox)x(..)&#x  & ♦ 1 2 2 |  2  2 1  2 1 |  1  1  2  1 0 | * 16 * *
(..).(..) (o.)o(o.)4(o.)x(o.)&#xt   ♦ 2 0 4 |  0  8 0  0 4 |  0  8  0  0 0 | *  * 2 *
(.o)q(.o) (..).(..) (.x)x(.x)&#xt   ♦ 0 4 4 |  0  0 2  8 2 |  0  0  0  4 2 | *  * * 4

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