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
Dihedral angles
  • at {4} between cube and hip:   arccos(-sqrt(2/3)) = 144.735610°
  • at {4} between cube and op:   135°
  • at {4} between hip and op:   arccos(-1/sqrt(3)) = 125.264390°
  • at {4} between cube and girco:   90°
  • at {6} between girco and hip:   90°
  • at {8} between girco and op:   90°
Confer
blends:
sirpdo  
general polytopal classes:
segmentochora  
External
links
hedrondude   wikipedia   polytopewiki  

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

The blend of 4 gircopes results in sirpdo.


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

snubbed forms: x2s3s4x, x s3s4s

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

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