Acronym	srox
Name	small rhombated hexeract, cantellated hexeract
Circumradius	sqrt[(7+4 sqrt(2))/2] = 2.515637
Inradius wrt. penp	sqrt[(57+40 sqrt(2))/20] = 2.382945
Inradius wrt. rix	sqrt[(17+12 sqrt(2))/6] = 2.379445
Inradius wrt. sirn	(1+sqrt(2))/2 = 1.207107
Lace city in approx. ASCII-art	©   o3x3o4x o3o3x4x o3o3x4x o3x3o4x -- o3o3x3o4x (sirn) o3o3x4x o3o3o4w o3o3o4w o3o3x4x -- o3o3o3x4x (tan) o3o3x4x o3o3o4w o3o3o4w o3o3x4x -- o3o3o3x4x (tan) o3x3o4x o3o3x4x o3o3x4x o3x3o4x -- o3o3x3o4x (sirn)
Coordinates	((1+sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2)   & all permutations, all changes of sign
Volume	[4426+3141 sqrt(2)]/45 = 197.067662
Dihedral angles (at margins)	at pen between penp and rix:   arccos[-sqrt(5/6)] = 155.905157° at tepe between penp and sirn:   arccos[-1/sqrt(5)] = 116.565051° at rap between rix and sirn:   arccos[-1/sqrt(6)] = 114.094843° at srit between sirn and sirn:   90°
Face vector	960, 4800, 7280, 4960, 1788, 268
Confer	variations: rerax   general polytopal classes: Wythoffian polypeta   analogs: rhombated hypercube rbCn
External links

As abstract polytope srox is isomorphic to qrax, thereby replacing sirco by querco, srit by qrit, and sirn by quarn.

Incidence matrix according to Dynkin symbol

o3o3o3x3o4x

. . . . . . | 960 |    8   2 |   12    4    8   1 |    8   6   12   4 |   2   4   8  6 |  1   2  4
------------+-----+----------+--------------------+-------------------+----------------+----------
. . . x . . |   2 | 3840   * |    3    1    1   0 |    3   3    3   1 |   1   3   3  3 |  1   1  3
. . . . . x |   2 |    * 960 |    0    0    4   1 |    0   0    6   4 |   0   0   4  6 |  0   1  4
------------+-----+----------+--------------------+-------------------+----------------+----------
. . o3x . . |   3 |    3   0 | 3840    *    *   * |    2   1    1   0 |   1   2   2  1 |  1   1  2
. . . x3o . |   3 |    3   0 |    * 1280    *   * |    0   3    0   1 |   0   3   0  3 |  1   0  3
. . . x . x |   4 |    2   2 |    *    * 1920   * |    0   0    3   1 |   0   0   3  3 |  0   1  3
. . . . o4x |   4 |    0   4 |    *    *    * 240 ♦    0   0    0   4 |   0   0   0  6 |  0   0  4
------------+-----+----------+--------------------+-------------------+----------------+----------
. o3o3x . . ♦   4 |    6   0 |    4    0    0   0 | 1920   *    *   * |   1   1   1  0 |  1   1  1
. . o3x3o . ♦   6 |   12   0 |    4    4    0   0 |    * 960    *   * |   0   2   0  1 |  1   0  2
. . o3x . x ♦   6 |    6   3 |    2    0    3   0 |    *   * 1920   * |   0   0   2  1 |  0   1  2
. . . x3o4x ♦  24 |   24  24 |    0    8   12   6 |    *   *    * 160 |   0   0   0  3 |  0   0  3
------------+-----+----------+--------------------+-------------------+----------------+----------
o3o3o3x . . ♦   5 |   10   0 |   10    0    0   0 |    5   0    0   0 | 384   *   *  * |  1   1  0
. o3o3x3o . ♦  10 |   30   0 |   20   10    0   0 |    5   5    0   0 |   * 384   *  * |  1   0  1
. o3o3x . x ♦   8 |   12   4 |    8    0    6   0 |    2   0    4   0 |   *   * 960  * |  0   1  1
. . o3x3o4x ♦  96 |  192  96 |   64   64   96  24 |    0  16   32   8 |   *   *   * 60 |  0   0  2
------------+-----+----------+--------------------+-------------------+----------------+----------
o3o3o3x3o . ♦  15 |   60   0 |   60   20    0   0 |   30  15    0   0 |   6   6   0  0 | 64   *  *
o3o3o3x . x ♦  10 |   20   5 |   20    0   10   0 |   10   0   10   0 |   2   0   5  0 |  * 192  *
. o3o3x3o4x ♦ 320 |  960 320 |  640  320  480  80 |  160 160  320  40 |   0  32  80 10 |  *   * 12

snubbed forms: o3o3o3x3o4s

oooo3oooo3xoox3oxxo4xxxx&#xt   → outer heights = 1/sqrt(2) = 0.707107
                                 inner height = 1
(sirn || pseudo tan || pseudo tan || sirn)

...

oxo4wxx ooo3xoo3oxo4xxw&#zx   → height = 0
(tegum sum of (w-{4},srit)-duoprism and ({8},tat)-duoprism and ({4},w-tes)-duoprism)

...