Acronym recarnit
Name retrocellirhombated penteractitriacontaditeron
Circumradius sqrt[17+8 sqrt(2)]/2 = 2.660531
Coordinates (1+2 sqrt(2), 1+sqrt(2), 1+sqrt(2), 1, 1)/2   & all permutations, all changes of sign
General of army carnit
Colonel of regiment carnit
Face vector 960, 3840, 3920, 1280, 142
Confer
general polytopal classes:
Wythoffian polytera  
External
links 		polytopewiki

As abstract polytope recarnit is isomorphic to garcornit, thereby replacing octagons by octagrams, resp. socco by gocco, tic by quith, and girco by quitco, resp. rawvatoth by wavitoth, sichado by gichado, and siphado by giphado.


Incidence matrix according to Dynkin symbol

    4/3    
   x---o   
  4 \ / 3  
     x     
  3 / \ 3  
   x---o   
    3/2    

x4x4/3o3*a3x3/2o3*a

. .   .    .   .    | 960 |    4   2   2 |   4   2   2   4   1   4   1 |  2  2  4   1   2   2   2   2 |  1  2  2  1  1
--------------------+-----+--------------+-----------------------------+------------------------------+---------------
x .   .    .   .    |   2 | 1920   *   * |   1   1   1   1   0   0   0 |  1  1  1   1   1   1   0   0 |  1  1  1  1  0
. x   .    .   .    |   2 |    * 960   * |   2   0   0   0   1   2   0 |  2  1  2   0   0   0   2   1 |  1  2  1  0  1
. .   .    .   x    |   2 |    *   * 960 |   0   0   0   2   0   2   1 |  0  0  2   0   1   2   1   2 |  0  1  2  1  1
--------------------+-----+--------------+-----------------------------+------------------------------+---------------
x4x   .    .   .    |   8 |    4   4   0 | 480   *   *   *   *   *   * |  1  1  1   0   0   0   0   0 |  1  1  1  0  0
x .   o3*a .   .    |   3 |    3   0   0 |   * 640   *   *   *   *   * |  1  0  0   1   1   0   0   0 |  1  1  0  1  0
x .   . *a3o   .    |   3 |    3   0   0 |   *   * 640   *   *   *   * |  0  1  0   1   0   1   0   0 |  1  0  1  1  0
x .   .    .   x3*a |   6 |    3   0   3 |   *   *   * 640   *   *   * |  0  0  1   0   1   1   0   0 |  0  1  1  1  0
. x4/3o    .   .    |   4 |    0   4   0 |   *   *   *   * 240   *   * |  2  0  0   0   0   0   2   0 |  1  2  0  0  1
. x   .    .   x    |   4 |    0   2   2 |   *   *   *   *   * 960   * |  0  0  1   0   0   0   1   1 |  0  1  1  0  1
. .   .    o3/2x    |   3 |    0   0   3 |   *   *   *   *   *   * 320 |  0  0  0   0   0   2   0   2 |  0  0  2  1  1
--------------------+-----+--------------+-----------------------------+------------------------------+---------------
x4x4/3o3*a .   .    ♦  24 |   24  24   0 |   6   8   0   0   6   0   0 | 80  *  *   *   *   *   *   * |  1  1  0  0  0
x4x   . *a3o   .    ♦  24 |   24  12   0 |   6   0   8   0   0   0   0 |  * 80  *   *   *   *   *   * |  1  0  1  0  0
x4x   .    .   x3*a ♦  48 |   24  24  24 |   6   0   0   8   0  12   0 |  *  * 80   *   *   *   *   * |  0  1  1  0  0
x .   o3*a3o   .    ♦   6 |   12   0   0 |   0   4   4   0   0   0   0 |  *  *  * 160   *   *   *   * |  1  0  0  1  0
x .   o3*a .   x3*a ♦  12 |   12   0   6 |   0   4   0   4   0   0   0 |  *  *  *   * 160   *   *   * |  0  1  0  1  0
x .   . *a3o3/2x3*a ♦  12 |   12   0  12 |   0   0   4   4   0   0   4 |  *  *  *   *   * 160   *   * |  0  0  1  1  0
. x4/3o    .   x    ♦   8 |    0   8   4 |   0   0   0   0   2   4   0 |  *  *  *   *   *   * 240   * |  0  1  0  0  1
. x   .    o3/2x    ♦   6 |    0   3   6 |   0   0   0   0   0   3   2 |  *  *  *   *   *   *   * 320 |  0  0  1  0  1
--------------------+-----+--------------+-----------------------------+------------------------------+---------------
x4x4/3o3*a3o   .    ♦  96 |  192  96   0 |  48  64  64   0  24   0   0 |  8  8  0  16   0   0   0   0 | 10  *  *  *  *
x4x4/3o3*a .   x3*a ♦ 192 |  192 192  96 |  48  64   0  64  48  96   0 |  8  0  8   0  16   0  24   0 |  * 10  *  *  *
x4x   . *a3o3/2x3*a ♦ 192 |  192  96 192 |  48   0  64  64   0  96  64 |  0  8  8   0   0  16   0  32 |  *  * 10  *  *
x .   o3*a3o3/2x3*a ♦  30 |   60   0  30 |   0  20  20  20   0   0  10 |  0  0  0   5   5   5   0   0 |  *  *  * 32  *
. x4/3o    o3/2x    ♦  12 |    0  12  12 |   0   0   0   0   3  12   4 |  0  0  0   0   0   0   3   4 |  *  *  *  * 80


     4     
   x---o   
  4 \ / 3/2
     x     
  3 / \ 3  
   x---o   
    3/2    

x4x4o3/2*a3x3/2o3*a

. . .      .   .    | 960 |    4   2   2 |   4   2   2   4   1   4   1 |  2  2  4   1   2   2   2   2 |  1  2  2  1  1
--------------------+-----+--------------+-----------------------------+------------------------------+---------------
x . .      .   .    |   2 | 1920   *   * |   1   1   1   1   0   0   0 |  1  1  1   1   1   1   0   0 |  1  1  1  1  0
. x .      .   .    |   2 |    * 960   * |   2   0   0   0   1   2   0 |  2  1  2   0   0   0   2   1 |  1  2  1  0  1
. . .      .   x    |   2 |    *   * 960 |   0   0   0   2   0   2   1 |  0  0  2   0   1   2   1   2 |  0  1  2  1  1
--------------------+-----+--------------+-----------------------------+------------------------------+---------------
x4x .      .   .    |   8 |    4   4   0 | 480   *   *   *   *   *   * |  1  1  1   0   0   0   0   0 |  1  1  1  0  0
x . o3/2*a .   .    |   3 |    3   0   0 |   * 640   *   *   *   *   * |  1  0  0   1   1   0   0   0 |  1  1  0  1  0
x . .   *a3o   .    |   3 |    3   0   0 |   *   * 640   *   *   *   * |  0  1  0   1   0   1   0   0 |  1  0  1  1  0
x . .      .   x3*a |   6 |    3   0   3 |   *   *   * 640   *   *   * |  0  0  1   0   1   1   0   0 |  0  1  1  1  0
. x4o      .   .    |   4 |    0   4   0 |   *   *   *   * 240   *   * |  2  0  0   0   0   0   2   0 |  1  2  0  0  1
. x .      .   x    |   4 |    0   2   2 |   *   *   *   *   * 960   * |  0  0  1   0   0   0   1   1 |  0  1  1  0  1
. . .      o3/2x    |   3 |    0   0   3 |   *   *   *   *   *   * 320 |  0  0  0   0   0   2   0   2 |  0  0  2  1  1
--------------------+-----+--------------+-----------------------------+------------------------------+---------------
x4x4o3/2*a .   .    ♦  24 |   24  24   0 |   6   8   0   0   6   0   0 | 80  *  *   *   *   *   *   * |  1  1  0  0  0
x4x .   *a3o   .    ♦  24 |   24  12   0 |   6   0   8   0   0   0   0 |  * 80  *   *   *   *   *   * |  1  0  1  0  0
x4x .      .   x3*a ♦  48 |   24  24  24 |   6   0   0   8   0  12   0 |  *  * 80   *   *   *   *   * |  0  1  1  0  0
x . o3/2*a3o   .    ♦   6 |   12   0   0 |   0   4   4   0   0   0   0 |  *  *  * 160   *   *   *   * |  1  0  0  1  0
x . o3/2*a .   x3*a ♦  12 |   12   0   6 |   0   4   0   4   0   0   0 |  *  *  *   * 160   *   *   * |  0  1  0  1  0
x . .   *a3o3/2x3*a ♦  12 |   12   0  12 |   0   0   4   4   0   0   4 |  *  *  *   *   * 160   *   * |  0  0  1  1  0
. x4o      .   x    ♦   8 |    0   8   4 |   0   0   0   0   2   4   0 |  *  *  *   *   *   * 240   * |  0  1  0  0  1
. x .      o3/2x    ♦   6 |    0   3   6 |   0   0   0   0   0   3   2 |  *  *  *   *   *   *   * 320 |  0  0  1  0  1
--------------------+-----+--------------+-----------------------------+------------------------------+---------------
x4x4o3/2*a3o   .    ♦  96 |  192  96   0 |  48  64  64   0  24   0   0 |  8  8  0  16   0   0   0   0 | 10  *  *  *  *
x4x4o3/2*a .   x3*a ♦ 192 |  192 192  96 |  48  64   0  64  48  96   0 |  8  0  8   0  16   0  24   0 |  * 10  *  *  *
x4x .   *a3o3/2x3*a ♦ 192 |  192  96 192 |  48   0  64  64   0  96  64 |  0  8  8   0   0  16   0  32 |  *  * 10  *  *
x . o3/2*a3o3/2x3*a ♦  30 |   60   0  30 |   0  20  20  20   0   0  10 |  0  0  0   5   5   5   0   0 |  *  *  * 32  *
. x4o      o3/2x    ♦  12 |    0  12  12 |   0   0   0   0   3  12   4 |  0  0  0   0   0   0   3   4 |  *  *  *  * 80


    4/3    
   x---o   
  4 \ / 3  
     x     
  3 / \ 3/2
   x---o   
     3     

x4x4/3o3*a3x3o3/2*a

. .   .    . .      | 960 |    4   2   2 |   4   2   2   4   1   4   1 |  2  2  4   1   2   2   2   2 |  1  2  2  1  1
--------------------+-----+--------------+-----------------------------+------------------------------+---------------
x .   .    . .      |   2 | 1920   *   * |   1   1   1   1   0   0   0 |  1  1  1   1   1   1   0   0 |  1  1  1  1  0
. x   .    . .      |   2 |    * 960   * |   2   0   0   0   1   2   0 |  2  1  2   0   0   0   2   1 |  1  2  1  0  1
. .   .    . x      |   2 |    *   * 960 |   0   0   0   2   0   2   1 |  0  0  2   0   1   2   1   2 |  0  1  2  1  1
--------------------+-----+--------------+-----------------------------+------------------------------+---------------
x4x   .    . .      |   8 |    4   4   0 | 480   *   *   *   *   *   * |  1  1  1   0   0   0   0   0 |  1  1  1  0  0
x .   o3*a . .      |   3 |    3   0   0 |   * 640   *   *   *   *   * |  1  0  0   1   1   0   0   0 |  1  1  0  1  0
x .   . *a3o .      |   3 |    3   0   0 |   *   * 640   *   *   *   * |  0  1  0   1   0   1   0   0 |  1  0  1  1  0
x .   .    . x3/2*a |   6 |    3   0   3 |   *   *   * 640   *   *   * |  0  0  1   0   1   1   0   0 |  0  1  1  1  0
. x4/3o    . .      |   4 |    0   4   0 |   *   *   *   * 240   *   * |  2  0  0   0   0   0   2   0 |  1  2  0  0  1
. x   .    . x      |   4 |    0   2   2 |   *   *   *   *   * 960   * |  0  0  1   0   0   0   1   1 |  0  1  1  0  1
. .   .    o3x      |   3 |    0   0   3 |   *   *   *   *   *   * 320 |  0  0  0   0   0   2   0   2 |  0  0  2  1  1
--------------------+-----+--------------+-----------------------------+------------------------------+---------------
x4x4/3o3*a . .      ♦  24 |   24  24   0 |   6   8   0   0   6   0   0 | 80  *  *   *   *   *   *   * |  1  1  0  0  0
x4x   . *a3o .      ♦  24 |   24  12   0 |   6   0   8   0   0   0   0 |  * 80  *   *   *   *   *   * |  1  0  1  0  0
x4x   .    . x3/2*a ♦  48 |   24  24  24 |   6   0   0   8   0  12   0 |  *  * 80   *   *   *   *   * |  0  1  1  0  0
x .   o3*a3o .      ♦   6 |   12   0   0 |   0   4   4   0   0   0   0 |  *  *  * 160   *   *   *   * |  1  0  0  1  0
x .   o3*a . x3/2*a ♦  12 |   12   0   6 |   0   4   0   4   0   0   0 |  *  *  *   * 160   *   *   * |  0  1  0  1  0
x .   . *a3o3x3/2*a ♦  12 |   12   0  12 |   0   0   4   4   0   0   4 |  *  *  *   *   * 160   *   * |  0  0  1  1  0
. x4/3o    . x      ♦   8 |    0   8   4 |   0   0   0   0   2   4   0 |  *  *  *   *   *   * 240   * |  0  1  0  0  1
. x   .    o3x      ♦   6 |    0   3   6 |   0   0   0   0   0   3   2 |  *  *  *   *   *   *   * 320 |  0  0  1  0  1
--------------------+-----+--------------+-----------------------------+------------------------------+---------------
x4x4/3o3*a3o .      ♦  96 |  192  96   0 |  48  64  64   0  24   0   0 |  8  8  0  16   0   0   0   0 | 10  *  *  *  *
x4x4/3o3*a . x3/2*a ♦ 192 |  192 192  96 |  48  64   0  64  48  96   0 |  8  0  8   0  16   0  24   0 |  * 10  *  *  *
x4x   . *a3o3x3/2*a ♦ 192 |  192  96 192 |  48   0  64  64   0  96  64 |  0  8  8   0   0  16   0  32 |  *  * 10  *  *
x .   o3*a3o3x3/2*a ♦  30 |   60   0  30 |   0  20  20  20   0   0  10 |  0  0  0   5   5   5   0   0 |  *  *  * 32  *
. x4/3o    o3x      ♦  12 |    0  12  12 |   0   0   0   0   3  12   4 |  0  0  0   0   0   0   3   4 |  *  *  *  * 80


     4     
   x---o   
  4 \ / 3/2
     x     
  3 / \ 3/2
   x---o   
     3     

x4x4o3/2*a3x3o3*a

. . .      . .      | 960 |    4   2   2 |   4   2   2   4   1   4   1 |  2  2  4   1   2   2   2   2 |  1  2  2  1  1
--------------------+-----+--------------+-----------------------------+------------------------------+---------------
x . .      . .      |   2 | 1920   *   * |   1   1   1   1   0   0   0 |  1  1  1   1   1   1   0   0 |  1  1  1  1  0
. x .      . .      |   2 |    * 960   * |   2   0   0   0   1   2   0 |  2  1  2   0   0   0   2   1 |  1  2  1  0  1
. . .      . x      |   2 |    *   * 960 |   0   0   0   2   0   2   1 |  0  0  2   0   1   2   1   2 |  0  1  2  1  1
--------------------+-----+--------------+-----------------------------+------------------------------+---------------
x4x .      . .      |   8 |    4   4   0 | 480   *   *   *   *   *   * |  1  1  1   0   0   0   0   0 |  1  1  1  0  0
x . o3/2*a . .      |   3 |    3   0   0 |   * 640   *   *   *   *   * |  1  0  0   1   1   0   0   0 |  1  1  0  1  0
x . .   *a3o .      |   3 |    3   0   0 |   *   * 640   *   *   *   * |  0  1  0   1   0   1   0   0 |  1  0  1  1  0
x . .      . x3/2*a |   6 |    3   0   3 |   *   *   * 640   *   *   * |  0  0  1   0   1   1   0   0 |  0  1  1  1  0
. x4o      . .      |   4 |    0   4   0 |   *   *   *   * 240   *   * |  2  0  0   0   0   0   2   0 |  1  2  0  0  1
. x .      . x      |   4 |    0   2   2 |   *   *   *   *   * 960   * |  0  0  1   0   0   0   1   1 |  0  1  1  0  1
. . .      o3x      |   3 |    0   0   3 |   *   *   *   *   *   * 320 |  0  0  0   0   0   2   0   2 |  0  0  2  1  1
--------------------+-----+--------------+-----------------------------+------------------------------+---------------
x4x4o3/2*a . .      ♦  24 |   24  24   0 |   6   8   0   0   6   0   0 | 80  *  *   *   *   *   *   * |  1  1  0  0  0
x4x .   *a3o .      ♦  24 |   24  12   0 |   6   0   8   0   0   0   0 |  * 80  *   *   *   *   *   * |  1  0  1  0  0
x4x .      . x3/2*a ♦  48 |   24  24  24 |   6   0   0   8   0  12   0 |  *  * 80   *   *   *   *   * |  0  1  1  0  0
x . o3/2*a3o .      ♦   6 |   12   0   0 |   0   4   4   0   0   0   0 |  *  *  * 160   *   *   *   * |  1  0  0  1  0
x . o3/2*a . x3/2*a ♦  12 |   12   0   6 |   0   4   0   4   0   0   0 |  *  *  *   * 160   *   *   * |  0  1  0  1  0
x . .   *a3o3x3/2*a ♦  12 |   12   0  12 |   0   0   4   4   0   0   4 |  *  *  *   *   * 160   *   * |  0  0  1  1  0
. x4o      . x      ♦   8 |    0   8   4 |   0   0   0   0   2   4   0 |  *  *  *   *   *   * 240   * |  0  1  0  0  1
. x .      o3x      ♦   6 |    0   3   6 |   0   0   0   0   0   3   2 |  *  *  *   *   *   *   * 320 |  0  0  1  0  1
--------------------+-----+--------------+-----------------------------+------------------------------+---------------
x4x4o3/2*a3o .      ♦  96 |  192  96   0 |  48  64  64   0  24   0   0 |  8  8  0  16   0   0   0   0 | 10  *  *  *  *
x4x4o3/2*a . x3/2*a ♦ 192 |  192 192  96 |  48  64   0  64  48  96   0 |  8  0  8   0  16   0  24   0 |  * 10  *  *  *
x4x .   *a3o3x3/2*a ♦ 192 |  192  96 192 |  48   0  64  64   0  96  64 |  0  8  8   0   0  16   0  32 |  *  * 10  *  *
x . o3/2*a3o3x3/2*a ♦  30 |   60   0  30 |   0  20  20  20   0   0  10 |  0  0  0   5   5   5   0   0 |  *  *  * 32  *
. x4o      o3x      ♦  12 |    0  12  12 |   0   0   0   0   3  12   4 |  0  0  0   0   0   0   3   4 |  *  *  *  * 80

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