Acronym prin
Name prismatorhombated penteract,
runcicantellated penteract
Field of sections
 ©
Circumradius sqrt[23+10 sqrt(2)]/2 = 3.047217
Vertex figure
 ©    ©
Lace city
in approx. ASCII-art
 ©  
x3o4x  u3o4x  x3x4x    x3x4x  u3o4x  x3o4x		-- x3x3o4x (prit)
                                          
                                          
                                          
u3o4x         o3u4x    o3u4x         u3o4x		-- o3u3o4x ((u,x)-srit)
                                          
                                          
                                          
x3x4x  o3u4x  o3x4w    o3x4w  o3u4x  x3x4x		-- o3x3x4x (grit)
                                          
                                          
                                          
                                          
                                          
x3x4x  o3u4x  o3x4w    o3x4w  o3u4x  x3x4x		-- o3x3x4x (grit)
                                          
                                          
                                          
u3o4x         o3u4x    o3u4x         u3o4x		-- o3u3o4x ((u,x)-srit)
                                          
                                          
                                          
x3o4x  u3o4x  x3x4x    x3x4x  u3o4x  x3o4x		-- x3x3o4x (prit)
Coordinates ((1+2 sqrt(2))/2, (1+2 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 – uniform polyteral members:
by cells: deca grit prit sichado tisdip tuttip
sibtadin 3210010800
prin 3201008080
& others)
Confer
related segmentotera:
grittip  
general polytopal classes:
partial Stott expansions  
External
links
hedrondude   wikipedia   polytopewiki  

As abstract polyteron prin is isomorph to quiprin, thereby replacing prograde by retrograde squares, resp. sirco by querco, resp. prit by paqrit.


Incidence matrix according to Dynkin symbol

o3x3x3o4x

. . . . . | 960 |   2   2   2 |   1   4   4   1   2   1 |   2   2   2   4   2  1 |  1  2  1  2
----------+-----+-------------+-------------------------+------------------------+------------
. x . . . |   2 | 960   *   * |   1   2   2   0   0   0 |   2   2   1   2   1  0 |  1  2  1  1
. . x . . |   2 |   * 960   * |   0   2   0   1   1   0 |   1   0   2   2   0  1 |  1  1  0  2
. . . . x |   2 |   *   * 960 |   0   0   2   0   1   1 |   0   1   0   2   2  1 |  0  1  1  2
----------+-----+-------------+-------------------------+------------------------+------------
o3x . . . |   3 |   3   0   0 | 320   *   *   *   *   * |   2   2   0   0   0  0 |  1  2  1  0
. x3x . . |   6 |   3   3   0 |   * 640   *   *   *   * |   1   0   1   1   0  0 |  1  1  0  1
. x . . x |   4 |   2   0   2 |   *   * 960   *   *   * |   0   1   0   1   1  0 |  0  1  1  1
. . x3o . |   3 |   0   3   0 |   *   *   * 320   *   * |   0   0   2   0   0  1 |  1  0  0  2
. . x . x |   4 |   0   2   2 |   *   *   *   * 480   * |   0   0   0   2   0  1 |  0  1  0  2
. . . o4x |   4 |   0   0   4 |   *   *   *   *   * 240 |   0   0   0   0   2  1 |  0  0  1  2
----------+-----+-------------+-------------------------+------------------------+------------
o3x3x . .   12 |  12   6   0 |   4   4   0   0   0   0 | 160   *   *   *   *  * |  1  1  0  0
o3x . . x    6 |   6   0   3 |   2   0   3   0   0   0 |   * 320   *   *   *  * |  0  1  1  0
. x3x3o .   12 |   6  12   0 |   0   4   0   4   0   0 |   *   * 160   *   *  * |  1  0  0  1
. x3x . x   12 |   6   6   6 |   0   2   3   0   3   0 |   *   *   * 320   *  * |  0  1  0  1
. x . o4x    8 |   4   0   8 |   0   0   4   0   0   2 |   *   *   *   * 240  * |  0  0  1  1
. . x3o4x   24 |   0  24  24 |   0   0   0   8  12   6 |   *   *   *   *   * 40 |  0  0  0  2
----------+-----+-------------+-------------------------+------------------------+------------
o3x3x3o .   30 |  30  30   0 |  10  20   0  10   0   0 |   5   0   5   0   0  0 | 32  *  *  *
o3x3x . x   24 |  24  12  12 |   8   8  12   0   6   0 |   2   4   0   4   0  0 |  * 80  *  *
o3x . o4x   12 |  12   0  12 |   4   0  12   0   0   3 |   0   4   0   0   3  0 |  *  * 80  *
. x3x3o4x  192 |  96 192 192 |   0  64  96  64  96  48 |   0   0  16  32  24  8 |  *  *  * 10

snubbed forms: o3x3x3o4s

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