Acronym	fawdint
Name	frustisphenary dispenteractitriacontaditeron, fastegiverted dispenteractitriacontaditeron
Field of sections	©
Circumradius	sqrt(2)-1/2 = 0.914214
Vertex figure	©
Coordinates	(sqrt(2)-1, sqrt(2)-1, 1, 1, 1)/2   & all permutations, all changes of sign
Colonel of regiment	(is itself locally convex – uniform polyteral members: by facets: gaqript gittith goccope grohp ope quidpith rap tisdip tistodip wavitoth gatopin 10 0 0 40 0 0 0 0 0 0 gipbin 0 10 40 0 80 0 32 80 80 0 fawdint 0 10 0 0 0 0 32 0 0 10 quappin 0 0 0 0 80 10 32 80 0 0 & others)
Face vector	320, 1440, 1440, 480, 52
Confer	general polytopal classes: Wythoffian polytera
External links

As abstract polytope fawdint is isomorphic to sirpin, thereby replacing octagrams by octagons, resp. quith by tic and gocco by socco, resp. gittith by steth and wavitoth by rawvatoth.

Incidence matrix according to Dynkin symbol

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

o3x3o3o *b4/3x4*c

. . . .      .    | 320 |   6   3 |   3   6   6   3 |   3  3   2  6  1 |  1  3  2
------------------+-----+---------+-----------------+------------------+---------
. x . .      .    |   2 | 960   * |   1   2   1   0 |   2  1   1  2  0 |  1  2  1
. . . .      x    |   2 |   * 480 |   0   0   2   2 |   0  1   0  4  1 |  0  2  2
------------------+-----+---------+-----------------+------------------+---------
o3x . .      .    |   3 |   3   0 | 320   *   *   * |   2  1   0  0  0 |  1  2  0
. x3o .      .    |   3 |   3   0 |   * 640   *   * |   1  0   1  1  0 |  1  1  1
. x . . *b4/3x    |   8 |   4   4 |   *   * 240   * |   0  1   0  2  0 |  0  2  1
. . o .      x4*c |   4 |   0   4 |   *   *   * 240 |   0  0   0  2  1 |  0  1  2
------------------+-----+---------+-----------------+------------------+---------
o3x3o .      .    ♦   6 |  12   0 |   4   4   0   0 | 160  *   *  *  * |  1  1  0
o3x . . *b4/3x    ♦  24 |  24  12 |   8   0   6   0 |   * 40   *  *  * |  0  2  0
. x3o3o      .    ♦   4 |   6   0 |   0   4   0   0 |   *  * 160  *  * |  1  0  1
. x3o . *b4/3x4*c ♦  24 |  24  24 |   0   8   6   6 |   *  *   * 80  * |  0  1  1
. . o3o      x4*c ♦   8 |   0  12 |   0   0   0   6 |   *  *   *  * 40 |  0  0  2
------------------+-----+---------+-----------------+------------------+---------
o3x3o3o      .    ♦  10 |  30   0 |  10  20   0   0 |   5  0   5  0  0 | 32  *  *
o3x3o . *b4/3x4*c ♦  96 | 192  96 |  64  64  48  24 |  16  8   0  8  0 |  * 10  *
. x3o3o *b4/3x4*c ♦  64 |  96  96 |   0  64  24  48 |   0  0  16  8  8 |  *  * 10

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

o3x3o3/2o *b4/3x4*c

. . .   .      .    | 320 |   6   3 |   3   6   6   3 |   3  3   2  6  1 |  1  3  2
--------------------+-----+---------+-----------------+------------------+---------
. x .   .      .    |   2 | 960   * |   1   2   1   0 |   2  1   1  2  0 |  1  2  1
. . .   .      x    |   2 |   * 480 |   0   0   2   2 |   0  1   0  4  1 |  0  2  2
--------------------+-----+---------+-----------------+------------------+---------
o3x .   .      .    |   3 |   3   0 | 320   *   *   * |   2  1   0  0  0 |  1  2  0
. x3o   .      .    |   3 |   3   0 |   * 640   *   * |   1  0   1  1  0 |  1  1  1
. x .   . *b4/3x    |   8 |   4   4 |   *   * 240   * |   0  1   0  2  0 |  0  2  1
. . o   .      x4*c |   4 |   0   4 |   *   *   * 240 |   0  0   0  2  1 |  0  1  2
--------------------+-----+---------+-----------------+------------------+---------
o3x3o   .      .    ♦   6 |  12   0 |   4   4   0   0 | 160  *   *  *  * |  1  1  0
o3x .   . *b4/3x    ♦  24 |  24  12 |   8   0   6   0 |   * 40   *  *  * |  0  2  0
. x3o3/2o      .    ♦   4 |   6   0 |   0   4   0   0 |   *  * 160  *  * |  1  0  1
. x3o   . *b4/3x4*c ♦  24 |  24  24 |   0   8   6   6 |   *  *   * 80  * |  0  1  1
. . o3/2o      x4*c ♦   8 |   0  12 |   0   0   0   6 |   *  *   *  * 40 |  0  0  2
--------------------+-----+---------+-----------------+------------------+---------
o3x3o3/2o      .    ♦  10 |  30   0 |  10  20   0   0 |   5  0   5  0  0 | 32  *  *
o3x3o   . *b4/3x4*c ♦  96 | 192  96 |  64  64  48  24 |  16  8   0  8  0 |  * 10  *
. x3o3/2o *b4/3x4*c ♦  64 |  96  96 |   0  64  24  48 |   0  0  16  8  8 |  *  * 10

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

o3/2x3o3o *b4/3x4*c

.   . . .      .    | 320 |   6   3 |   3   6   6   3 |   3  3   2  6  1 |  1  3  2
--------------------+-----+---------+-----------------+------------------+---------
.   x . .      .    |   2 | 960   * |   1   2   1   0 |   2  1   1  2  0 |  1  2  1
.   . . .      x    |   2 |   * 480 |   0   0   2   2 |   0  1   0  4  1 |  0  2  2
--------------------+-----+---------+-----------------+------------------+---------
o3/2x . .      .    |   3 |   3   0 | 320   *   *   * |   2  1   0  0  0 |  1  2  0
.   x3o .      .    |   3 |   3   0 |   * 640   *   * |   1  0   1  1  0 |  1  1  1
.   x . . *b4/3x    |   8 |   4   4 |   *   * 240   * |   0  1   0  2  0 |  0  2  1
.   . o .      x4*c |   4 |   0   4 |   *   *   * 240 |   0  0   0  2  1 |  0  1  2
--------------------+-----+---------+-----------------+------------------+---------
o3/2x3o .      .    ♦   6 |  12   0 |   4   4   0   0 | 160  *   *  *  * |  1  1  0
o3/2x . . *b4/3x    ♦  24 |  24  12 |   8   0   6   0 |   * 40   *  *  * |  0  2  0
.   x3o3o      .    ♦   4 |   6   0 |   0   4   0   0 |   *  * 160  *  * |  1  0  1
.   x3o . *b4/3x4*c ♦  24 |  24  24 |   0   8   6   6 |   *  *   * 80  * |  0  1  1
.   . o3o      x4*c ♦   8 |   0  12 |   0   0   0   6 |   *  *   *  * 40 |  0  0  2
--------------------+-----+---------+-----------------+------------------+---------
o3/2x3o3o      .    ♦  10 |  30   0 |  10  20   0   0 |   5  0   5  0  0 | 32  *  *
o3/2x3o . *b4/3x4*c ♦  96 | 192  96 |  64  64  48  24 |  16  8   0  8  0 |  * 10  *
.   x3o3o *b4/3x4*c ♦  64 |  96  96 |   0  64  24  48 |   0  0  16  8  8 |  *  * 10

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

o3/2x3o3/2o *b4/3x4*c

.   . .   .      .    | 320 |   6   3 |   3   6   6   3 |   3  3   2  6  1 |  1  3  2
----------------------+-----+---------+-----------------+------------------+---------
.   x .   .      .    |   2 | 960   * |   1   2   1   0 |   2  1   1  2  0 |  1  2  1
.   . .   .      x    |   2 |   * 480 |   0   0   2   2 |   0  1   0  4  1 |  0  2  2
----------------------+-----+---------+-----------------+------------------+---------
o3/2x .   .      .    |   3 |   3   0 | 320   *   *   * |   2  1   0  0  0 |  1  2  0
.   x3o   .      .    |   3 |   3   0 |   * 640   *   * |   1  0   1  1  0 |  1  1  1
.   x .   . *b4/3x    |   8 |   4   4 |   *   * 240   * |   0  1   0  2  0 |  0  2  1
.   . o   .      x4*c |   4 |   0   4 |   *   *   * 240 |   0  0   0  2  1 |  0  1  2
----------------------+-----+---------+-----------------+------------------+---------
o3/2x3o   .      .    ♦   6 |  12   0 |   4   4   0   0 | 160  *   *  *  * |  1  1  0
o3/2x .   . *b4/3x    ♦  24 |  24  12 |   8   0   6   0 |   * 40   *  *  * |  0  2  0
.   x3o3/2o      .    ♦   4 |   6   0 |   0   4   0   0 |   *  * 160  *  * |  1  0  1
.   x3o   . *b4/3x4*c ♦  24 |  24  24 |   0   8   6   6 |   *  *   * 80  * |  0  1  1
.   . o3/2o      x4*c ♦   8 |   0  12 |   0   0   0   6 |   *  *   *  * 40 |  0  0  2
----------------------+-----+---------+-----------------+------------------+---------
o3/2x3o3/2o      .    ♦  10 |  30   0 |  10  20   0   0 |   5  0   5  0  0 | 32  *  *
o3/2x3o   . *b4/3x4*c ♦  96 | 192  96 |  64  64  48  24 |  16  8   0  8  0 |  * 10  *
.   x3o3/2o *b4/3x4*c ♦  64 |  96  96 |   0  64  24  48 |   0  0  16  8  8 |  *  * 10

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

o3x3/2o3o *b4/3x4/3*c

. .   . .      .      | 320 |   6   3 |   3   6   6   3 |   3  3   2  6  1 |  1  3  2
----------------------+-----+---------+-----------------+------------------+---------
. x   . .      .      |   2 | 960   * |   1   2   1   0 |   2  1   1  2  0 |  1  2  1
. .   . .      x      |   2 |   * 480 |   0   0   2   2 |   0  1   0  4  1 |  0  2  2
----------------------+-----+---------+-----------------+------------------+---------
o3x   . .      .      |   3 |   3   0 | 320   *   *   * |   2  1   0  0  0 |  1  2  0
. x3/2o .      .      |   3 |   3   0 |   * 640   *   * |   1  0   1  1  0 |  1  1  1
. x   . . *b4/3x      |   8 |   4   4 |   *   * 240   * |   0  1   0  2  0 |  0  2  1
. .   o .      x4/3*c |   4 |   0   4 |   *   *   * 240 |   0  0   0  2  1 |  0  1  2
----------------------+-----+---------+-----------------+------------------+---------
o3x3/2o .      .      ♦   6 |  12   0 |   4   4   0   0 | 160  *   *  *  * |  1  1  0
o3x   . . *b4/3x      ♦  24 |  24  12 |   8   0   6   0 |   * 40   *  *  * |  0  2  0
. x3/2o3o      .      ♦   4 |   6   0 |   0   4   0   0 |   *  * 160  *  * |  1  0  1
. x3/2o . *b4/3x4/3*c ♦  24 |  24  24 |   0   8   6   6 |   *  *   * 80  * |  0  1  1
. .   o3o      x4/3*c ♦   8 |   0  12 |   0   0   0   6 |   *  *   *  * 40 |  0  0  2
----------------------+-----+---------+-----------------+------------------+---------
o3x3/2o3o      .      ♦  10 |  30   0 |  10  20   0   0 |   5  0   5  0  0 | 32  *  *
o3x3/2o . *b4/3x4/3*c ♦  96 | 192  96 |  64  64  48  24 |  16  8   0  8  0 |  * 10  *
. x3/2o3o *b4/3x4/3*c ♦  64 |  96  96 |   0  64  24  48 |   0  0  16  8  8 |  *  * 10

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

o3x3/2o3/2o *b4/3x4/3*c

. .   .   .      .      | 320 |   6   3 |   3   6   6   3 |   3  3   2  6  1 |  1  3  2
------------------------+-----+---------+-----------------+------------------+---------
. x   .   .      .      |   2 | 960   * |   1   2   1   0 |   2  1   1  2  0 |  1  2  1
. .   .   .      x      |   2 |   * 480 |   0   0   2   2 |   0  1   0  4  1 |  0  2  2
------------------------+-----+---------+-----------------+------------------+---------
o3x   .   .      .      |   3 |   3   0 | 320   *   *   * |   2  1   0  0  0 |  1  2  0
. x3/2o   .      .      |   3 |   3   0 |   * 640   *   * |   1  0   1  1  0 |  1  1  1
. x   .   . *b4/3x      |   8 |   4   4 |   *   * 240   * |   0  1   0  2  0 |  0  2  1
. .   o   .      x4/3*c |   4 |   0   4 |   *   *   * 240 |   0  0   0  2  1 |  0  1  2
------------------------+-----+---------+-----------------+------------------+---------
o3x3/2o   .      .      ♦   6 |  12   0 |   4   4   0   0 | 160  *   *  *  * |  1  1  0
o3x   .   . *b4/3x      ♦  24 |  24  12 |   8   0   6   0 |   * 40   *  *  * |  0  2  0
. x3/2o3/2o      .      ♦   4 |   6   0 |   0   4   0   0 |   *  * 160  *  * |  1  0  1
. x3/2o   . *b4/3x4/3*c ♦  24 |  24  24 |   0   8   6   6 |   *  *   * 80  * |  0  1  1
. .   o3/2o      x4/3*c ♦   8 |   0  12 |   0   0   0   6 |   *  *   *  * 40 |  0  0  2
------------------------+-----+---------+-----------------+------------------+---------
o3x3/2o3/2o      .      ♦  10 |  30   0 |  10  20   0   0 |   5  0   5  0  0 | 32  *  *
o3x3/2o   . *b4/3x4/3*c ♦  96 | 192  96 |  64  64  48  24 |  16  8   0  8  0 |  * 10  *
. x3/2o3/2o *b4/3x4/3*c ♦  64 |  96  96 |   0  64  24  48 |   0  0  16  8  8 |  *  * 10

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

o3/2x3/2o3o *b4/3x4/3*c

.   .   . .      .      | 320 |   6   3 |   3   6   6   3 |   3  3   2  6  1 |  1  3  2
------------------------+-----+---------+-----------------+------------------+---------
.   x   . .      .      |   2 | 960   * |   1   2   1   0 |   2  1   1  2  0 |  1  2  1
.   .   . .      x      |   2 |   * 480 |   0   0   2   2 |   0  1   0  4  1 |  0  2  2
------------------------+-----+---------+-----------------+------------------+---------
o3/2x   . .      .      |   3 |   3   0 | 320   *   *   * |   2  1   0  0  0 |  1  2  0
.   x3/2o .      .      |   3 |   3   0 |   * 640   *   * |   1  0   1  1  0 |  1  1  1
.   x   . . *b4/3x      |   8 |   4   4 |   *   * 240   * |   0  1   0  2  0 |  0  2  1
.   .   o .      x4/3*c |   4 |   0   4 |   *   *   * 240 |   0  0   0  2  1 |  0  1  2
------------------------+-----+---------+-----------------+------------------+---------
o3/2x3/2o .      .      ♦   6 |  12   0 |   4   4   0   0 | 160  *   *  *  * |  1  1  0
o3/2x   . . *b4/3x      ♦  24 |  24  12 |   8   0   6   0 |   * 40   *  *  * |  0  2  0
.   x3/2o3o      .      ♦   4 |   6   0 |   0   4   0   0 |   *  * 160  *  * |  1  0  1
.   x3/2o . *b4/3x4/3*c ♦  24 |  24  24 |   0   8   6   6 |   *  *   * 80  * |  0  1  1
.   .   o3o      x4/3*c ♦   8 |   0  12 |   0   0   0   6 |   *  *   *  * 40 |  0  0  2
------------------------+-----+---------+-----------------+------------------+---------
o3/2x3/2o3o      .      ♦  10 |  30   0 |  10  20   0   0 |   5  0   5  0  0 | 32  *  *
o3/2x3/2o . *b4/3x4/3*c ♦  96 | 192  96 |  64  64  48  24 |  16  8   0  8  0 |  * 10  *
.   x3/2o3o *b4/3x4/3*c ♦  64 |  96  96 |   0  64  24  48 |   0  0  16  8  8 |  *  * 10

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

o3/2x3/2o3/2o *b4/3x4/3*c

.   .   .   .      .      | 320 |   6   3 |   3   6   6   3 |   3  3   2  6  1 |  1  3  2
--------------------------+-----+---------+-----------------+------------------+---------
.   x   .   .      .      |   2 | 960   * |   1   2   1   0 |   2  1   1  2  0 |  1  2  1
.   .   .   .      x      |   2 |   * 480 |   0   0   2   2 |   0  1   0  4  1 |  0  2  2
--------------------------+-----+---------+-----------------+------------------+---------
o3/2x   .   .      .      |   3 |   3   0 | 320   *   *   * |   2  1   0  0  0 |  1  2  0
.   x3/2o   .      .      |   3 |   3   0 |   * 640   *   * |   1  0   1  1  0 |  1  1  1
.   x   .   . *b4/3x      |   8 |   4   4 |   *   * 240   * |   0  1   0  2  0 |  0  2  1
.   .   o   .      x4/3*c |   4 |   0   4 |   *   *   * 240 |   0  0   0  2  1 |  0  1  2
--------------------------+-----+---------+-----------------+------------------+---------
o3/2x3/2o   .      .      ♦   6 |  12   0 |   4   4   0   0 | 160  *   *  *  * |  1  1  0
o3/2x   .   . *b4/3x      ♦  24 |  24  12 |   8   0   6   0 |   * 40   *  *  * |  0  2  0
.   x3/2o3/2o      .      ♦   4 |   6   0 |   0   4   0   0 |   *  * 160  *  * |  1  0  1
.   x3/2o   . *b4/3x4/3*c ♦  24 |  24  24 |   0   8   6   6 |   *  *   * 80  * |  0  1  1
.   .   o3/2o      x4/3*c ♦   8 |   0  12 |   0   0   0   6 |   *  *   *  * 40 |  0  0  2
--------------------------+-----+---------+-----------------+------------------+---------
o3/2x3/2o3/2o      .      ♦  10 |  30   0 |  10  20   0   0 |   5  0   5  0  0 | 32  *  *
o3/2x3/2o   . *b4/3x4/3*c ♦  96 | 192  96 |  64  64  48  24 |  16  8   0  8  0 |  * 10  *
.   x3/2o3/2o *b4/3x4/3*c ♦  64 |  96  96 |   0  64  24  48 |   0  0  16  8  8 |  *  * 10