Acronym rawn (old: rawvanant)
Name retrosphenary penteract
Circumradius sqrt[11+6 sqrt(2)]/2 = 2.207107
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 sirn
Colonel of regiment sirn
Face vector 320, 1280, 1280, 440, 52
Confer
general polytopal classes:
Wythoffian polytera  
External
links 		polytopewiki

As abstract polytope rawn is isomorphic to wavinant, thereby replacing octagons by octagrams, resp. tic by quith and socco by gocco, resp. tat by quitit and rawvatoth by wavitoth. – As such rawn is a lieutenant.


Incidence matrix according to Dynkin symbol

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

o3o3x3o4/3x4*c

. . . .   .    | 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 .   x4*c |   8 |   4   4 |   *   * 240  * |   0   0  2  1 |  0  1  2
. . . o4/3x    |   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 .   x4*c ♦  24 |  24  12 |   8   0   6  0 |   *   * 80  * |  0  1  1
. . x3o4/3x4*c ♦  24 |  24  24 |   0   8   6  6 |   *   *  * 40 |  0  0  2
---------------+-----+---------+----------------+---------------+---------
o3o3x3o   .    ♦  10 |  30   0 |  20  10   0  0 |   5   5  0  0 | 32  *  *
o3o3x .   x4*c ♦  64 |  96  32 |  64   0  24  0 |  16   0  8  0 |  * 10  *
. o3x3o4/3x4*c ♦  96 | 192  96 |  64  64  48 24 |   0  16  8  8 |  *  * 10


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

o3o3x3/2o4x4*c

. . .   . .    | 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
. . x3/2o .    |   3 |   3   0 |   * 320   *  * |   0   2  0  1 |  1  0  2
. . x   . x4*c |   8 |   4   4 |   *   * 240  * |   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
. o3x3/2o .    ♦   6 |  12   0 |   4   4   0  0 |   * 160  *  * |  1  0  1
. o3x   . x4*c ♦  24 |  24  12 |   8   0   6  0 |   *   * 80  * |  0  1  1
. . x3/2o4x4*c ♦  24 |  24  24 |   0   8   6  6 |   *   *  * 40 |  0  0  2
---------------+-----+---------+----------------+---------------+---------
o3o3x3/2o .    ♦  10 |  30   0 |  20  10   0  0 |   5   5  0  0 | 32  *  *
o3o3x   . x4*c ♦  64 |  96  32 |  64   0  24  0 |  16   0  8  0 |  * 10  *
. o3x3/2o4x4*c ♦  96 | 192  96 |  64  64  48 24 |   0  16  8  8 |  *  * 10


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

o3o3/2x3o4/3x4*c

. .   . .   .    | 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
-----------------+-----+---------+----------------+---------------+---------
. o3/2x .   .    |   3 |   3   0 | 640   *   *  * |   1   1  1  0 |  1  1  1
. .   x3o   .    |   3 |   3   0 |   * 320   *  * |   0   2  0  1 |  1  0  2
. .   x .   x4*c |   8 |   4   4 |   *   * 240  * |   0   0  2  1 |  0  1  2
. .   . o4/3x    |   4 |   0   4 |   *   *   * 80 |   0   0  0  3 |  0  0  3
-----------------+-----+---------+----------------+---------------+---------
o3o3/2x .   .    ♦   4 |   6   0 |   4   0   0  0 | 160   *  *  * |  1  1  0
. o3/2x3o   .    ♦   6 |  12   0 |   4   4   0  0 |   * 160  *  * |  1  0  1
. o3/2x .   x4*c ♦  24 |  24  12 |   8   0   6  0 |   *   * 80  * |  0  1  1
. .   x3o4/3x4*c ♦  24 |  24  24 |   0   8   6  6 |   *   *  * 40 |  0  0  2
-----------------+-----+---------+----------------+---------------+---------
o3o3/2x3o   .    ♦  10 |  30   0 |  20  10   0  0 |   5   5  0  0 | 32  *  *
o3o3/2x .   x4*c ♦  64 |  96  32 |  64   0  24  0 |  16   0  8  0 |  * 10  *
. o3/2x3o4/3x4*c ♦  96 | 192  96 |  64  64  48 24 |   0  16  8  8 |  *  * 10


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

o3o3/2x3/2o4x4*c

. .   .   . .    | 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
-----------------+-----+---------+----------------+---------------+---------
. o3/2x   . .    |   3 |   3   0 | 640   *   *  * |   1   1  1  0 |  1  1  1
. .   x3/2o .    |   3 |   3   0 |   * 320   *  * |   0   2  0  1 |  1  0  2
. .   x   . x4*c |   8 |   4   4 |   *   * 240  * |   0   0  2  1 |  0  1  2
. .   .   o4x    |   4 |   0   4 |   *   *   * 80 |   0   0  0  3 |  0  0  3
-----------------+-----+---------+----------------+---------------+---------
o3o3/2x   . .    ♦   4 |   6   0 |   4   0   0  0 | 160   *  *  * |  1  1  0
. o3/2x3/2o .    ♦   6 |  12   0 |   4   4   0  0 |   * 160  *  * |  1  0  1
. o3/2x   . x4*c ♦  24 |  24  12 |   8   0   6  0 |   *   * 80  * |  0  1  1
. .   x3/2o4x4*c ♦  24 |  24  24 |   0   8   6  6 |   *   *  * 40 |  0  0  2
-----------------+-----+---------+----------------+---------------+---------
o3o3/2x3/2o .    ♦  10 |  30   0 |  20  10   0  0 |   5   5  0  0 | 32  *  *
o3o3/2x   . x4*c ♦  64 |  96  32 |  64   0  24  0 |  16   0  8  0 |  * 10  *
. o3/2x3/2o4x4*c ♦  96 | 192  96 |  64  64  48 24 |   0  16  8  8 |  *  * 10


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

o3/2o3x3o4/3x4*c

.   . . .   .    | 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 .   x4*c |   8 |   4   4 |   *   * 240  * |   0   0  2  1 |  0  1  2
.   . . o4/3x    |   4 |   0   4 |   *   *   * 80 |   0   0  0  3 |  0  0  3
-----------------+-----+---------+----------------+---------------+---------
o3/2o3x .   .    ♦   4 |   6   0 |   4   0   0  0 | 160   *  *  * |  1  1  0
.   o3x3o   .    ♦   6 |  12   0 |   4   4   0  0 |   * 160  *  * |  1  0  1
.   o3x .   x4*c ♦  24 |  24  12 |   8   0   6  0 |   *   * 80  * |  0  1  1
.   . x3o4/3x4*c ♦  24 |  24  24 |   0   8   6  6 |   *   *  * 40 |  0  0  2
-----------------+-----+---------+----------------+---------------+---------
o3/2o3x3o   .    ♦  10 |  30   0 |  20  10   0  0 |   5   5  0  0 | 32  *  *
o3/2o3x .   x4*c ♦  64 |  96  32 |  64   0  24  0 |  16   0  8  0 |  * 10  *
.   o3x3o4/3x4*c ♦  96 | 192  96 |  64  64  48 24 |   0  16  8  8 |  *  * 10


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

o3/2o3x3/2o4x4*c

.   . .   . .    | 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
.   . x3/2o .    |   3 |   3   0 |   * 320   *  * |   0   2  0  1 |  1  0  2
.   . x   . x4*c |   8 |   4   4 |   *   * 240  * |   0   0  2  1 |  0  1  2
.   . .   o4x    |   4 |   0   4 |   *   *   * 80 |   0   0  0  3 |  0  0  3
-----------------+-----+---------+----------------+---------------+---------
o3/2o3x   . .    ♦   4 |   6   0 |   4   0   0  0 | 160   *  *  * |  1  1  0
.   o3x3/2o .    ♦   6 |  12   0 |   4   4   0  0 |   * 160  *  * |  1  0  1
.   o3x   . x4*c ♦  24 |  24  12 |   8   0   6  0 |   *   * 80  * |  0  1  1
.   . x3/2o4x4*c ♦  24 |  24  24 |   0   8   6  6 |   *   *  * 40 |  0  0  2
-----------------+-----+---------+----------------+---------------+---------
o3/2o3x3/2o .    ♦  10 |  30   0 |  20  10   0  0 |   5   5  0  0 | 32  *  *
o3/2o3x   . x4*c ♦  64 |  96  32 |  64   0  24  0 |  16   0  8  0 |  * 10  *
.   o3x3/2o4x4*c ♦  96 | 192  96 |  64  64  48 24 |   0  16  8  8 |  *  * 10


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

o3/2o3/2x3o4/3x4*c

.   .   . .   .    | 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
-------------------+-----+---------+----------------+---------------+---------
.   o3/2x .   .    |   3 |   3   0 | 640   *   *  * |   1   1  1  0 |  1  1  1
.   .   x3o   .    |   3 |   3   0 |   * 320   *  * |   0   2  0  1 |  1  0  2
.   .   x .   x4*c |   8 |   4   4 |   *   * 240  * |   0   0  2  1 |  0  1  2
.   .   . o4/3x    |   4 |   0   4 |   *   *   * 80 |   0   0  0  3 |  0  0  3
-------------------+-----+---------+----------------+---------------+---------
o3/2o3/2x .   .    ♦   4 |   6   0 |   4   0   0  0 | 160   *  *  * |  1  1  0
.   o3/2x3o   .    ♦   6 |  12   0 |   4   4   0  0 |   * 160  *  * |  1  0  1
.   o3/2x .   x4*c ♦  24 |  24  12 |   8   0   6  0 |   *   * 80  * |  0  1  1
.   .   x3o4/3x4*c ♦  24 |  24  24 |   0   8   6  6 |   *   *  * 40 |  0  0  2
-------------------+-----+---------+----------------+---------------+---------
o3/2o3/2x3o   .    ♦  10 |  30   0 |  20  10   0  0 |   5   5  0  0 | 32  *  *
o3/2o3/2x .   x4*c ♦  64 |  96  32 |  64   0  24  0 |  16   0  8  0 |  * 10  *
.   o3/2x3o4/3x4*c ♦  96 | 192  96 |  64  64  48 24 |   0  16  8  8 |  *  * 10


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

o3/2o3/2x3/2o4x4*c

.   .   .   . .    | 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
-------------------+-----+---------+----------------+---------------+---------
.   o3/2x   . .    |   3 |   3   0 | 640   *   *  * |   1   1  1  0 |  1  1  1
.   .   x3/2o .    |   3 |   3   0 |   * 320   *  * |   0   2  0  1 |  1  0  2
.   .   x   . x4*c |   8 |   4   4 |   *   * 240  * |   0   0  2  1 |  0  1  2
.   .   .   o4x    |   4 |   0   4 |   *   *   * 80 |   0   0  0  3 |  0  0  3
-------------------+-----+---------+----------------+---------------+---------
o3/2o3/2x   . .    ♦   4 |   6   0 |   4   0   0  0 | 160   *  *  * |  1  1  0
.   o3/2x3/2o .    ♦   6 |  12   0 |   4   4   0  0 |   * 160  *  * |  1  0  1
.   o3/2x   . x4*c ♦  24 |  24  12 |   8   0   6  0 |   *   * 80  * |  0  1  1
.   .   x3/2o4x4*c ♦  24 |  24  24 |   0   8   6  6 |   *   *  * 40 |  0  0  2
-------------------+-----+---------+----------------+---------------+---------
o3/2o3/2x3/2o .    ♦  10 |  30   0 |  20  10   0  0 |   5   5  0  0 | 32  *  *
o3/2o3/2x   . x4*c ♦  64 |  96  32 |  64   0  24  0 |  16   0  8  0 |  * 10  *
.   o3/2x3/2o4x4*c ♦  96 | 192  96 |  64  64  48 24 |   0  16  8  8 |  *  * 10

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