Acronym ticcup, K-4.99
Name truncated-cube prism
Segmentochoron display
Cross sections
 ©
Circumradius sqrt[2+sqrt(2)] = 1.847759
Coordinates ((1+sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2)   & all permutations in all but last coord., all changes of sign
Dihedral angles
  • at {4} between op and trip:   arccos(-1/sqrt(3)) = 125.264390°
  • at {4} between op and op:   90°
  • at {8} between op and tic:   90°
  • at {3} between tic and trip:   90°
Confer
uniform relative:
spic  
related segmentochora:
{4} || op  
related CRFs:
dapabdi spic  
general polytopal classes:
segmentochora  
External
links
hedrondude  

As abstract polytope ticcup is isomorphic to quithip, thereby replacing octagons by octagrams, resp. replacing op by stop and tic by quith.

Ticcup could be gyro-augmented by {4} || op sementochora to obtain dapabdi spic, i.e. the oct-first central bistratic segment of spic. – The prefix "gyro" thereby refers to the chosen orientation of the squares (i.e. the augmentations): being aligned as the co-squares of o3x4o x would be.


Incidence matrix according to Dynkin symbol

x o3x4x

. . . . | 48 |  1  2  1 |  2  1  1  2 | 1 2 1
--------+----+----------+-------------+------
x . . . |  2 | 24  *  * |  2  1  0  0 | 1 2 0
. . x . |  2 |  * 48  * |  1  0  1  1 | 1 1 1
. . . x |  2 |  *  * 24 |  0  1  0  2 | 0 2 1
--------+----+----------+-------------+------
x . x . |  4 |  2  2  0 | 24  *  *  * | 1 1 0
x . . x |  4 |  2  0  2 |  * 12  *  * | 0 2 0
. o3x . |  3 |  0  3  0 |  *  * 16  * | 1 0 1
. . x4x |  8 |  0  4  4 |  *  *  * 12 | 0 1 1
--------+----+----------+-------------+------
x o3x .   6 |  3  6  0 |  3  0  2  0 | 8 * *
x . x4x  16 |  8  8  8 |  4  4  0  2 | * 6 *
. o3x4x  24 |  0 24 12 |  0  0  8  6 | * * 2

x o3/2x4x

. .   . . | 48 |  1  2  1 |  2  1  1  2 | 1 2 1
----------+----+----------+-------------+------
x .   . . |  2 | 24  *  * |  2  1  0  0 | 1 2 0
. .   x . |  2 |  * 48  * |  1  0  1  1 | 1 1 1
. .   . x |  2 |  *  * 24 |  0  1  0  2 | 0 2 1
----------+----+----------+-------------+------
x .   x . |  4 |  2  2  0 | 24  *  *  * | 1 1 0
x .   . x |  4 |  2  0  2 |  * 12  *  * | 0 2 0
. o3/2x . |  3 |  0  3  0 |  *  * 16  * | 1 0 1
. .   x4x |  8 |  0  4  4 |  *  *  * 12 | 0 1 1
----------+----+----------+-------------+------
x o3/2x .   6 |  3  6  0 |  3  0  2  0 | 8 * *
x .   x4x  16 |  8  8  8 |  4  4  0  2 | * 6 *
. o3/2x4x  24 |  0 24 12 |  0  0  8  6 | * * 2

oo3xx4xx&#x   → height = 1
(tic || tic)

o.3o.4o.    | 24  * |  1  2  1  0  0 | 1 2  2  1 0 0 | 1 1 2 0
.o3.o4.o    |  * 24 |  0  0  1  2  1 | 0 0  2  1 1 2 | 0 1 2 1
------------+-------+----------------+---------------+--------
.. x. ..    |  2  0 | 24  *  *  *  * | 1 1  1  0 0 0 | 1 1 1 0
.. .. x.    |  2  0 |  * 12  *  *  * | 0 2  0  1 0 0 | 1 0 2 0
oo3oo4oo&#x |  1  1 |  *  * 24  *  * | 0 0  2  1 0 0 | 0 1 2 0
.. .x ..    |  0  2 |  *  *  * 24  * | 0 0  1  0 1 1 | 0 1 1 1
.. .. .x    |  0  2 |  *  *  *  * 12 | 0 0  0  1 0 2 | 0 0 2 1
------------+-------+----------------+---------------+--------
o.3x. ..    |  3  0 |  3  0  0  0  0 | 8 *  *  * * * | 1 1 0 0
.. x.4x.    |  8  0 |  4  4  0  0  0 | * 6  *  * * * | 1 0 1 0
.. xx ..&#x |  2  2 |  1  0  2  1  0 | * * 24  * * * | 0 1 1 0
.. .. xx&#x |  2  2 |  0  1  2  0  1 | * *  * 12 * * | 0 0 2 0
.o3.x ..    |  0  3 |  0  0  0  3  0 | * *  *  * 8 * | 0 1 0 1
.. .x4.x    |  0  8 |  0  0  0  4  4 | * *  *  * * 6 | 0 0 1 1
------------+-------+----------------+---------------+--------
o.3x.4x.     24  0 | 24 12  0  0  0 | 8 6  0  0 0 0 | 1 * * *
oo3xx ..&#x   3  3 |  3  0  3  3  0 | 1 0  3  0 1 0 | * 8 * *
.. xx4xx&#x   8  8 |  4  4  8  4  4 | 0 1  4  4 0 1 | * * 6 *
.o3.x4.x      0 24 |  0  0  0 24 12 | 0 0  0  0 8 6 | * * * 1

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