Acronym	gircope, K-4.125
Name	great-rhombicuboctahedron prism
Segmentochoron display
Cross sections	©
Circumradius	sqrt[(7+3 sqrt(2))/2] = 2.370932
Coordinates	((1+2 sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2)   & all permutations in all but last coord., all changes of sign
External links

As abstract polytope gircope is isomorphic to quitcope, thereby replacing octagons by octagrams, resp. replacing op by stop and girco by quitco.

Incidence matrix according to Dynkin symbol

x x3x4x

. . . . | 96 |  1  1  1  1 |  1  1  1  1  1  1 | 1  1 1 1
--------+----+-------------+-------------------+---------
x . . . |  2 | 48  *  *  * |  1  1  1  0  0  0 | 1  1 1 0
. x . . |  2 |  * 48  *  * |  1  0  0  1  1  0 | 1  1 0 1
. . x . |  2 |  *  * 48  * |  0  1  0  1  0  1 | 1  0 1 1
. . . x |  2 |  *  *  * 48 |  0  0  1  0  1  1 | 0  1 1 1
--------+----+-------------+-------------------+---------
x x . . |  4 |  2  2  0  0 | 24  *  *  *  *  * | 1  1 0 0
x . x . |  4 |  2  0  2  0 |  * 24  *  *  *  * | 1  0 1 0
x . . x |  4 |  2  0  0  2 |  *  * 24  *  *  * | 0  1 1 0
. x3x . |  6 |  0  3  3  0 |  *  *  * 16  *  * | 1  0 0 1
. x . x |  4 |  0  2  0  2 |  *  *  *  * 24  * | 0  1 0 1
. . x4x |  8 |  0  0  4  4 |  *  *  *  *  * 12 | 0  0 1 1
--------+----+-------------+-------------------+---------
x x3x . ♦ 12 |  6  6  6  0 |  3  3  0  2  0  0 | 8  * * *
x x . x ♦  8 |  4  4  0  4 |  2  0  2  0  2  0 | * 12 * *
x . x4x ♦ 16 |  8  0  8  8 |  0  4  4  0  0  2 | *  * 6 *
. x3x4x ♦ 48 |  0 24 24 24 |  0  0  0  8 12  6 | *  * * 2

xx3xx4xx&#x   → height = 1
(girco || girco)

o.3o.4o.    | 48  * |  1  1  1  1  0  0  0 | 1  1 1  1  1  1 0  0 0 | 1 1  1 1 0
.o3.o4.o    |  * 48 |  0  0  0  1  1  1  1 | 0  0 0  1  1  1 1  1 1 | 0 1  1 1 1
------------+-------+----------------------+------------------------+-----------
x. .. ..    |  2  0 | 24  *  *  *  *  *  * | 1  1 0  1  0  0 0  0 0 | 1 1  1 0 0
.. x. ..    |  2  0 |  * 24  *  *  *  *  * | 1  0 1  0  1  0 0  0 0 | 1 1  0 1 0
.. .. x.    |  2  0 |  *  * 24  *  *  *  * | 0  1 1  0  0  1 0  0 0 | 1 0  1 1 0
oo3oo4oo&#x |  1  1 |  *  *  * 48  *  *  * | 0  0 0  1  1  1 0  0 0 | 0 1  1 1 0
.x .. ..    |  0  2 |  *  *  *  * 24  *  * | 0  0 0  1  0  0 1  1 0 | 0 1  1 0 1
.. .x ..    |  0  2 |  *  *  *  *  * 24  * | 0  0 0  0  1  0 1  0 1 | 0 1  0 1 1
.. .. .x    |  0  2 |  *  *  *  *  *  * 24 | 0  0 0  0  0  1 0  1 1 | 0 0  1 1 1
------------+-------+----------------------+------------------------+-----------
x.3x. ..    |  6  0 |  3  3  0  0  0  0  0 | 8  * *  *  *  * *  * * | 1 1  0 0 0
x. .. x.    |  4  0 |  2  0  2  0  0  0  0 | * 12 *  *  *  * *  * * | 1 0  1 0 0
.. x.4x.    |  8  0 |  0  4  4  0  0  0  0 | *  * 6  *  *  * *  * * | 1 0  0 1 0
xx .. ..&#x |  2  2 |  1  0  0  2  1  0  0 | *  * * 24  *  * *  * * | 0 1  1 0 0
.. xx ..&#x |  2  2 |  0  1  0  2  0  1  0 | *  * *  * 24  * *  * * | 0 1  0 1 0
.. .. xx&#x |  2  2 |  0  0  1  2  0  0  1 | *  * *  *  * 24 *  * * | 0 0  1 1 0
.x3.x ..    |  0  6 |  0  0  0  0  3  3  0 | *  * *  *  *  * 8  * * | 0 1  0 0 1
.x .. .x    |  0  4 |  0  0  0  0  2  0  2 | *  * *  *  *  * * 12 * | 0 0  1 0 1
.. .x4.x    |  0  8 |  0  0  0  0  0  4  4 | *  * *  *  *  * *  * 6 | 0 0  0 1 1
------------+-------+----------------------+------------------------+-----------
x.3x.4x.    ♦ 48  0 | 24 24 24  0  0  0  0 | 8 12 6  0  0  0 0  0 0 | 1 *  * * *
xx3xx ..&#x ♦  6  6 |  3  3  0  6  3  3  0 | 1  0 0  3  3  0 1  0 0 | * 8  * * *
xx .. xx&#x ♦  4  4 |  2  0  2  4  2  0  2 | 0  1 0  2  0  2 0  1 0 | * * 12 * *
.. xx4xx&#x ♦  8  8 |  0  4  4  8  0  4  4 | 0  0 1  0  4  4 0  0 1 | * *  * 6 *
.x3.x4.x    ♦  0 48 |  0  0  0  0 24 24 24 | 0  0 0  0  0  0 8 12 6 | * *  * * 1