Acronym srox
Name small rhombated hexeract,
cantellated hexeract
Circumradius sqrt[(7+4 sqrt(2))/2] = 2.515637
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
External
links
wikipedia

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

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)

...

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