Acronym cytau tes
Name cyclotetraaugmented tesseract,
cyclotetradiminished icositetrachoron
Circumradius 1
Lace city
in approx. ASCII-art
x4o     x4o
           
    o4q    
           
x4o     x4o
o4o x4o o4o
           
x4o     x4o
           
o4o x4o o4o
Dihedral angles
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.


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

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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