Acronym sirn
Name small rhombated penteract,
cantellated penteract
Circumradius sqrt[11+6 sqrt(2)]/2 = 2.207107
Vertex figure
 ©
Lace city
in approx. ASCII-art
 ©  
x3o4x  o3x4x    o3x4x  x3o4x		-- o3x3o4x (srit)
                            
                            
                            
o3x4x  o3o4w    o3o4w  o3x4x		-- o3o3x4x (tat)
                            
                            
                            
                            
                            
o3x4x  o3o4w    o3o4w  o3x4x		-- o3o3x4x (tat)
                            
                            
                            
x3o4x  o3x4x    o3x4x  x3o4x		-- o3x3o4x (srit)
Coordinates ((1+sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2)   & all permutations, all changes of sign
General of army (is itself convex)
Colonel of regiment (is itself locally convex – other uniform polyteral members: rawn   & others)
Dihedral angles
(at margins)
Confer
related segmentotera:
sritatat   tattip  
general polytopal classes:
partial Stott expansions  
External
links
wikipedia   polytopewiki  

Incidence matrix according to Dynkin symbol

o3o3x3o4x

. . . . . | 320 |   6   2 |   6   3   6  1 |   2   3   6  3 |  1  2  3
----------+-----+---------+----------------+----------------+---------
. . x . . |   2 | 960   * |   2   1   1  0 |   1   2   2  1 |  1  1  2
. . . . x |   2 |   * 320 |   0   0   3  1 |   0   0   3  3 |  0  1  3
----------+-----+---------+----------------+----------------+---------
. o3x . . |   3 |   3   0 | 640   *   *  * |   1   1   1  0 |  1  1  1
. . x3o . |   3 |   3   0 |   * 320   *  * |   0   2   0  1 |  1  0  2
. . x . x |   4 |   2   2 |   *   * 480  * |   0   0   2  1 |  0  1  2
. . . o4x |   4 |   0   4 |   *   *   * 80 |   0   0   0  3 |  0  0  3
----------+-----+---------+----------------+----------------+---------
o3o3x . .    4 |   6   0 |   4   0   0  0 | 160   *   *  * |  1  1  0
. o3x3o .    6 |  12   0 |   4   4   0  0 |   * 160   *  * |  1  0  1
. o3x . x    6 |   6   3 |   2   0   3  0 |   *   * 320  * |  0  1  1
. . x3o4x   24 |  24  24 |   0   8  12  6 |   *   *   * 40 |  0  0  2
----------+-----+---------+----------------+----------------+---------
o3o3x3o .   10 |  30   0 |  20  10   0  0 |   5   5   0  0 | 32  *  *
o3o3x . x    8 |  12   4 |   8   0   6  0 |   2   0   4  0 |  * 80  *
. o3x3o4x   96 | 192  96 |  64  64  96 24 |   0  16  32  8 |  *  * 10

snubbed forms: o3o3x3o4s

oooo3xoox3oxxo4xxxx&#xt   → outer heights = 1/sqrt(2) = 0.707107
                            inner height = 1
(srit || pseudo tat || pseudo tat || srit)

o...3o...3o...4o...     & | 192   * |   4   2   2   0  0  0 |   2   2   4  1   4   1   2   0  0  0 |  1  2  2   2   2   4  1  0  0 | 1  1  2 2  0
.o..3.o..3.o..4.o..     & |   * 128 |   0   0   3   3  1  1 |   0   0   0  0   3   3   3   3  3  1 |  0  0  0   1   3   3  3  1  3 | 0  1  1 3  1
--------------------------+---------+-----------------------+--------------------------------------+-------------------------------+-------------
.... x... .... ....     & |   2   0 | 384   *   *   *  *  * |   1   1   1  0   1   0   0   0  0  0 |  1  1  1   1   1   1  0  0  0 | 1  1  1 1  0
.... .... .... x...     & |   2   0 |   * 192   *   *  *  * |   0   0   2  1   0   0   1   0  0  0 |  0  1  2   0   0   2  1  0  0 | 1  0  1 2  0
oo..3oo..3oo..4oo..&#x  & |   1   1 |   *   * 384   *  *  * |   0   0   0  0   2   1   1   0  0  0 |  0  0  0   1   2   2  1  0  0 | 0  1  1 2  0
.... .... .x.. ....     & |   0   2 |   *   *   * 192  *  * |   0   0   0  0   0   1   0   2  1  0 |  0  0  0   0   2   0  1  1  2 | 0  1  0 2  1
.... .... .... .x..     & |   0   2 |   *   *   *   * 64  * |   0   0   0  0   0   0   3   0  0  1 |  0  0  0   0   0   3  3  0  0 | 0  0  1 3  0
.oo.3.oo.3.oo.4.oo.&#x    |   0   2 |   *   *   *   *  * 64 |   0   0   0  0   0   0   0   0  3  1 |  0  0  0   0   0   0  3  0  3 | 0  0  0 3  1
--------------------------+---------+-----------------------+--------------------------------------+-------------------------------+-------------
o...3x... .... ....     & |   3   0 |   3   0   0   0  0  0 | 128   *   *  *   *   *   *   *  *  * |  1  1  0   1   0   0  0  0  0 | 1  1  1 0  0
.... x...3o... ....     & |   3   0 |   3   0   0   0  0  0 |   * 128   *  *   *   *   *   *  *  * |  1  0  1   0   1   0  0  0  0 | 1  1  0 1  0
.... x... .... x...     & |   4   0 |   2   2   0   0  0  0 |   *   * 192  *   *   *   *   *  *  * |  0  1  1   0   0   1  0  0  0 | 1  0  1 1  0
.... .... o...4x...     & |   4   0 |   0   4   0   0  0  0 |   *   *   * 48   *   *   *   *  *  * |  0  0  2   0   0   0  1  0  0 | 1  0  0 2  0
.... xo.. .... ....&#x  & |   2   1 |   1   0   2   0  0  0 |   *   *   *  * 384   *   *   *  *  * |  0  0  0   1   1   1  0  0  0 | 0  1  1 1  0
.... .... ox.. ....&#x  & |   1   2 |   0   0   2   1  0  0 |   *   *   *  *   * 192   *   *  *  * |  0  0  0   0   2   0  1  0  0 | 0  1  0 2  0
.... .... .... xx..&#x  & |   2   2 |   0   1   2   0  1  0 |   *   *   *  *   *   * 192   *  *  * |  0  0  0   0   0   2  1  0  0 | 0  0  1 2  0
.... .o..3.x.. ....     & |   0   3 |   0   0   0   3  0  0 |   *   *   *  *   *   *   * 128  *  * |  0  0  0   0   1   0  0  1  1 | 0  1  0 1  1
.... .... .xx. ....&#x    |   0   4 |   0   0   0   2  0  2 |   *   *   *  *   *   *   *   * 96  * |  0  0  0   0   0   0  1  0  2 | 0  0  0 2  1
.... .... .... .xx.&#x    |   0   4 |   0   0   0   0  2  2 |   *   *   *  *   *   *   *   *  * 32 |  0  0  0   0   0   0  3  0  0 | 0  0  0 3  0
--------------------------+---------+-----------------------+--------------------------------------+-------------------------------+-------------
o...3x...3o... ....     &    6   0 |  12   0   0   0  0  0 |   4   4   0  0   0   0   0   0  0  0 | 32  *  *   *   *   *  *  *  * | 1  1  0 0  0
o...3x... .... x...     &    6   0 |   6   3   0   0  0  0 |   2   0   3  0   0   0   0   0  0  0 |  * 64  *   *   *   *  *  *  * | 1  0  1 0  0
.... x...3o...4x...     &   24   0 |  24  24   0   0  0  0 |   0   8  12  6   0   0   0   0  0  0 |  *  * 16   *   *   *  *  *  * | 1  0  0 1  0
oo..3xo.. .... ....&#x  &    3   1 |   3   0   3   0  0  0 |   1   0   0  0   3   0   0   0  0  0 |  *  *  * 128   *   *  *  *  * | 0  1  1 0  0
.... xo..3ox.. ....&#x  &    3   3 |   3   0   6   3  0  0 |   0   1   0  0   3   3   0   1  0  0 |  *  *  *   * 128   *  *  *  * | 0  1  0 1  0
.... xo.. .... xx..&#x  &    4   2 |   2   2   4   0  1  0 |   0   0   1  0   2   0   2   0  0  0 |  *  *  *   *   * 192  *  *  * | 0  0  1 1  0
.... .... oxxo4xxxx&#xt      8  16 |   0   8  16   8  8  8 |   0   0   0  2   0   8   8   0  4  4 |  *  *  *   *   *   * 24  *  * | 0  0  0 2  0
.o..3.o..3.x.. ....     &    0   4 |   0   0   0   6  0  0 |   0   0   0  0   0   0   0   4  0  0 |  *  *  *   *   *   *  * 32  * | 0  1  0 0  1
.... .oo.3.xx. ....&#x       0   6 |   0   0   0   6  0  3 |   0   0   0  0   0   0   0   2  3  0 |  *  *  *   *   *   *  *  * 64 | 0  0  0 1  1
--------------------------+---------+-----------------------+--------------------------------------+-------------------------------+-------------
o...3x...3o...4x...     &   96   0 | 192  96   0   0  0  0 |  64  64  96 24   0   0   0   0  0  0 | 16 32  8   0   0   0  0  0  0 | 2  *  * *  *
oo..3xo..3ox.. ....&#x  &    6   4 |  12   0  12   6  0  0 |   4   4   0  0  12   6   0   4  0  0 |  1  0  0   4   4   0  0  1  0 | * 32  * *  *
oo..3xo.. .... xx..&#x  &    6   2 |   6   3   6   0  1  0 |   2   0   3  0   6   0   3   0  0  0 |  0  1  0   2   0   3  0  0  0 | *  * 64 *  *
.... xoox3oxxo4xxxx&#xt     48  48 |  48  48  96  48 24 24 |   0  16  24 12  48  48  48  16 24 12 |  0  0  2   0  16  24  6  0  8 | *  *  * 8  *
.oo.3.oo.3.xx. ....&#x       0   8 |   0   0   0  12  0  4 |   0   0   0  0   0   0   0   8  6  0 |  0  0  0   0   0   0  0  2  4 | *  *  * * 16

oxo4wxx xoo3oxo4xxw&#zx   → height = 0
(tegum sum of (w-{4},sirco)-duoprism and ({8},tic)-duoprism and ({4},w-cube)-duoprism)

...

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