Acronym ..., oct || cube, K-4.15
Name octahedron atop cube,
octahedral antiprism,
cubical antiprism,
vertex figure of icoap
Segmentochoron display
Circumradius sqrt[(4+sqrt(2))/7] = 0.879465
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • at {3} between tet and tet:   arccos[-(3 sqrt(2)-1)/4] = 144.160482°
  • at {3} between oct and tet:   arccos[-(3 sqrt(2)-2)/4] = 124.101465°
  • at {3} between squippy and tet:   arccos[-(3 sqrt(2)-2)/4] = 124.101465°
  • at {4} between cube and squippy:   arccos[-(2-sqrt(2))/2] = 107.031248°
Confer
related segmentochora:
{4} || gyro cube

Incidence matrix according to Dynkin symbol

xo3oo4ox&#x   → height = sqrt[2 sqrt(2)-1]/2 = 0.676097
(oct || cube)

o.3o.4o.    | 6 *   4  4  0 | 4  8  4 0 | 1 4  4 1 0
.o3.o4.o    | * 8 |  0  3  3 | 0  3  6 3 | 0 1  3 3 1
------------+-----+----------+-----------+-----------
x. .. ..    | 2 0 | 12  *  * | 2  2  0 0 | 1 2  1 0 0
oo3oo4oo&#x | 1 1 |  * 24  * | 0  2  2 0 | 0 1  2 1 0
.. .. .x    | 0 2 |  *  * 12 | 0  0  2 2 | 0 0  1 2 1
------------+-----+----------+-----------+-----------
x.3o. ..    | 3 0 |  3  0  0 | 8  *  * * | 1 1  0 0 0
xo .. ..&#x | 2 1 |  1  2  0 | * 24  * * | 0 1  1 0 0
.. .. ox&#x | 1 2 |  0  2  1 | *  * 24 * | 0 0  1 1 0
.. .o4.x    | 0 4 |  0  0  4 | *  *  * 6 | 0 0  0 1 1
------------+-----+----------+-----------+-----------
x.3o.4o.     6 0 | 12  0  0 | 8  0  0 0 | 1 *  * * *
xo3oo ..&#x  3 1 |  3  3  0 | 1  3  0 0 | * 8  * * *
xo .. ox&#x  2 2 |  1  4  1 | 0  2  2 0 | * * 12 * *
.. oo4ox&#x  1 4 |  0  4  4 | 0  0  4 1 | * *  * 6 *
.o3.o4.x     0 8 |  0  0 12 | 0  0  0 6 | * *  * * 1

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