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   wikipedia   polytopewiki  

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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