Acronym	sinnont
Name	small penteractipenteractitriacontiditeron
Field of sections	©
Circumradius	sqrt[7+2 sqrt(2)]/2 = 1.567516
Inradius wrt. pen	-[5+sqrt(2)]/sqrt(20) = -1.434262
Inradius wrt. tes	(1+sqrt(2))/2 = 1.207107
Inradius wrt. steth	1/2 = 0.5
Vertex figure	©
Coordinates	((1+sqrt(2))/2, 1/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign
Volume	[120+149 sqrt(2)]/30 = 11.023927
Surface	[125+120 sqrt(2)+sqrt(5)]/3 = 98.980565
General of army	scant
Colonel of regiment	scant
Dihedral angles (at margins)	at cube between steth and tes:   90° at socco between steth and steth:   90° at tet between pen and steth:   arccos[1/sqrt(5)] = 63.434949°
Face vector	160, 640, 640, 280, 52
Confer	general polytopal classes: Wythoffian polytera   analogs: socco series
External links

As abstract polytope sinnont is isomorphic to ginnont, thereby replacing octagons by octagrams, resp. socco by gocco and steth by gittith. – As such sinnont is a lieutenant.

Incidence matrix according to Dynkin symbol

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

o3o3o3x4x4/3*c

. . . . .      | 160 |   4   4 |   6   6  4 |   4  4  6 |  1  1  4
---------------+-----+---------+------------+-----------+---------
. . . x .      |   2 | 320   * |   3   0  1 |   3  0  3 |  1  0  3
. . . . x      |   2 |   * 320 |   0   3  1 |   0  3  3 |  0  1  3
---------------+-----+---------+------------+-----------+---------
. . o3x .      |   3 |   3   0 | 320   *  * |   2  0  1 |  1  0  2
. . o . x4/3*c |   4 |   0   4 |   * 240  * |   0  2  1 |  0  1  2
. . . x4x      |   8 |   4   4 |   *   * 80 |   0  0  3 |  0  0  3
---------------+-----+---------+------------+-----------+---------
. o3o3x .      ♦   4 |   6   0 |   4   0  0 | 160  *  * |  1  0  1
. o3o . x4/3*c ♦   8 |   0  12 |   0   6  0 |   * 80  * |  0  1  1
. . o3x4x4/3*c ♦  24 |  24  24 |   8   6  6 |   *  * 40 |  0  0  2
---------------+-----+---------+------------+-----------+---------
o3o3o3x .      ♦   5 |  10   0 |  10   0  0 |   5  0  0 | 32  *  *
o3o3o . x4/3*c ♦  16 |   0  32 |   0  24  0 |   0  8  0 |  * 10  *
. o3o3x4x4/3*c ♦  64 |  96  96 |  64  48 24 |  16  8  8 |  *  * 10

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

o3o3o3/2x4x4*c

. . .   . .    | 160 |   4   4 |   6   6  4 |   4  4  6 |  1  1  4
---------------+-----+---------+------------+-----------+---------
. . .   x .    |   2 | 320   * |   3   0  1 |   3  0  3 |  1  0  3
. . .   . x    |   2 |   * 320 |   0   3  1 |   0  3  3 |  0  1  3
---------------+-----+---------+------------+-----------+---------
. . o3/2x .    |   3 |   3   0 | 320   *  * |   2  0  1 |  1  0  2
. . o   . x4*c |   4 |   0   4 |   * 240  * |   0  2  1 |  0  1  2
. . .   x4x    |   8 |   4   4 |   *   * 80 |   0  0  3 |  0  0  3
---------------+-----+---------+------------+-----------+---------
. o3o3/2x .    ♦   4 |   6   0 |   4   0  0 | 160  *  * |  1  0  1
. o3o   . x4*c ♦   8 |   0  12 |   0   6  0 |   * 80  * |  0  1  1
. . o3/2x4x4*c ♦  24 |  24  24 |   8   6  6 |   *  * 40 |  0  0  2
---------------+-----+---------+------------+-----------+---------
o3o3o3/2x .    ♦   5 |  10   0 |  10   0  0 |   5  0  0 | 32  *  *
o3o3o   . x4*c ♦  16 |   0  32 |   0  24  0 |   0  8  0 |  * 10  *
. o3o3/2x4x4*c ♦  64 |  96  96 |  64  48 24 |  16  8  8 |  *  * 10

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

o3o3/2o3x4x4/3*c

. .   . . .      | 160 |   4   4 |   6   6  4 |   4  4  6 |  1  1  4
-----------------+-----+---------+------------+-----------+---------
. .   . x .      |   2 | 320   * |   3   0  1 |   3  0  3 |  1  0  3
. .   . . x      |   2 |   * 320 |   0   3  1 |   0  3  3 |  0  1  3
-----------------+-----+---------+------------+-----------+---------
. .   o3x .      |   3 |   3   0 | 320   *  * |   2  0  1 |  1  0  2
. .   o . x4/3*c |   4 |   0   4 |   * 240  * |   0  2  1 |  0  1  2
. .   . x4x      |   8 |   4   4 |   *   * 80 |   0  0  3 |  0  0  3
-----------------+-----+---------+------------+-----------+---------
. o3/2o3x .      ♦   4 |   6   0 |   4   0  0 | 160  *  * |  1  0  1
. o3/2o . x4/3*c ♦   8 |   0  12 |   0   6  0 |   * 80  * |  0  1  1
. .   o3x4x4/3*c ♦  24 |  24  24 |   8   6  6 |   *  * 40 |  0  0  2
-----------------+-----+---------+------------+-----------+---------
o3o3/2o3x .      ♦   5 |  10   0 |  10   0  0 |   5  0  0 | 32  *  *
o3o3/2o . x4/3*c ♦  16 |   0  32 |   0  24  0 |   0  8  0 |  * 10  *
. o3/2o3x4x4/3*c ♦  64 |  96  96 |  64  48 24 |  16  8  8 |  *  * 10

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

o3o3/2o3/2x4x4*c

. .   .   . .    | 160 |   4   4 |   6   6  4 |   4  4  6 |  1  1  4
-----------------+-----+---------+------------+-----------+---------
. .   .   x .    |   2 | 320   * |   3   0  1 |   3  0  3 |  1  0  3
. .   .   . x    |   2 |   * 320 |   0   3  1 |   0  3  3 |  0  1  3
-----------------+-----+---------+------------+-----------+---------
. .   o3/2x .    |   3 |   3   0 | 320   *  * |   2  0  1 |  1  0  2
. .   o   . x4*c |   4 |   0   4 |   * 240  * |   0  2  1 |  0  1  2
. .   .   x4x    |   8 |   4   4 |   *   * 80 |   0  0  3 |  0  0  3
-----------------+-----+---------+------------+-----------+---------
. o3/2o3/2x .    ♦   4 |   6   0 |   4   0  0 | 160  *  * |  1  0  1
. o3/2o   . x4*c ♦   8 |   0  12 |   0   6  0 |   * 80  * |  0  1  1
. .   o3/2x4x4*c ♦  24 |  24  24 |   8   6  6 |   *  * 40 |  0  0  2
-----------------+-----+---------+------------+-----------+---------
o3o3/2o3/2x .    ♦   5 |  10   0 |  10   0  0 |   5  0  0 | 32  *  *
o3o3/2o   . x4*c ♦  16 |   0  32 |   0  24  0 |   0  8  0 |  * 10  *
. o3/2o3/2x4x4*c ♦  64 |  96  96 |  64  48 24 |  16  8  8 |  *  * 10

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

o3/2o3o3x4x4/3*c

.   . . . .      | 160 |   4   4 |   6   6  4 |   4  4  6 |  1  1  4
-----------------+-----+---------+------------+-----------+---------
.   . . x .      |   2 | 320   * |   3   0  1 |   3  0  3 |  1  0  3
.   . . . x      |   2 |   * 320 |   0   3  1 |   0  3  3 |  0  1  3
-----------------+-----+---------+------------+-----------+---------
.   . o3x .      |   3 |   3   0 | 320   *  * |   2  0  1 |  1  0  2
.   . o . x4/3*c |   4 |   0   4 |   * 240  * |   0  2  1 |  0  1  2
.   . . x4x      |   8 |   4   4 |   *   * 80 |   0  0  3 |  0  0  3
-----------------+-----+---------+------------+-----------+---------
.   o3o3x .      ♦   4 |   6   0 |   4   0  0 | 160  *  * |  1  0  1
.   o3o . x4/3*c ♦   8 |   0  12 |   0   6  0 |   * 80  * |  0  1  1
.   . o3x4x4/3*c ♦  24 |  24  24 |   8   6  6 |   *  * 40 |  0  0  2
-----------------+-----+---------+------------+-----------+---------
o3/2o3o3x .      ♦   5 |  10   0 |  10   0  0 |   5  0  0 | 32  *  *
o3/2o3o . x4/3*c ♦  16 |   0  32 |   0  24  0 |   0  8  0 |  * 10  *
.   o3o3x4x4/3*c ♦  64 |  96  96 |  64  48 24 |  16  8  8 |  *  * 10

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

o3/2o3o3/2x4x4*c

.   . .   . .    | 160 |   4   4 |   6   6  4 |   4  4  6 |  1  1  4
-----------------+-----+---------+------------+-----------+---------
.   . .   x .    |   2 | 320   * |   3   0  1 |   3  0  3 |  1  0  3
.   . .   . x    |   2 |   * 320 |   0   3  1 |   0  3  3 |  0  1  3
-----------------+-----+---------+------------+-----------+---------
.   . o3/2x .    |   3 |   3   0 | 320   *  * |   2  0  1 |  1  0  2
.   . o   . x4*c |   4 |   0   4 |   * 240  * |   0  2  1 |  0  1  2
.   . .   x4x    |   8 |   4   4 |   *   * 80 |   0  0  3 |  0  0  3
-----------------+-----+---------+------------+-----------+---------
.   o3o3/2x .    ♦   4 |   6   0 |   4   0  0 | 160  *  * |  1  0  1
.   o3o   . x4*c ♦   8 |   0  12 |   0   6  0 |   * 80  * |  0  1  1
.   . o3/2x4x4*c ♦  24 |  24  24 |   8   6  6 |   *  * 40 |  0  0  2
-----------------+-----+---------+------------+-----------+---------
o3/2o3o3/2x .    ♦   5 |  10   0 |  10   0  0 |   5  0  0 | 32  *  *
o3/2o3o   . x4*c ♦  16 |   0  32 |   0  24  0 |   0  8  0 |  * 10  *
.   o3o3/2x4x4*c ♦  64 |  96  96 |  64  48 24 |  16  8  8 |  *  * 10

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

o3/2o3/2o3x4x4/3*c

.   .   . . .      | 160 |   4   4 |   6   6  4 |   4  4  6 |  1  1  4
-------------------+-----+---------+------------+-----------+---------
.   .   . x .      |   2 | 320   * |   3   0  1 |   3  0  3 |  1  0  3
.   .   . . x      |   2 |   * 320 |   0   3  1 |   0  3  3 |  0  1  3
-------------------+-----+---------+------------+-----------+---------
.   .   o3x .      |   3 |   3   0 | 320   *  * |   2  0  1 |  1  0  2
.   .   o . x4/3*c |   4 |   0   4 |   * 240  * |   0  2  1 |  0  1  2
.   .   . x4x      |   8 |   4   4 |   *   * 80 |   0  0  3 |  0  0  3
-------------------+-----+---------+------------+-----------+---------
.   o3/2o3x .      ♦   4 |   6   0 |   4   0  0 | 160  *  * |  1  0  1
.   o3/2o . x4/3*c ♦   8 |   0  12 |   0   6  0 |   * 80  * |  0  1  1
.   .   o3x4x4/3*c ♦  24 |  24  24 |   8   6  6 |   *  * 40 |  0  0  2
-------------------+-----+---------+------------+-----------+---------
o3/2o3/2o3x .      ♦   5 |  10   0 |  10   0  0 |   5  0  0 | 32  *  *
o3/2o3/2o . x4/3*c ♦  16 |   0  32 |   0  24  0 |   0  8  0 |  * 10  *
.   o3/2o3x4x4/3*c ♦  64 |  96  96 |  64  48 24 |  16  8  8 |  *  * 10

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

o3/2o3/2o3/2x4x4*c

.   .   .   . .    | 160 |   4   4 |   6   6  4 |   4  4  6 |  1  1  4
-------------------+-----+---------+------------+-----------+---------
.   .   .   x .    |   2 | 320   * |   3   0  1 |   3  0  3 |  1  0  3
.   .   .   . x    |   2 |   * 320 |   0   3  1 |   0  3  3 |  0  1  3
-------------------+-----+---------+------------+-----------+---------
.   .   o3/2x .    |   3 |   3   0 | 320   *  * |   2  0  1 |  1  0  2
.   .   o   . x4*c |   4 |   0   4 |   * 240  * |   0  2  1 |  0  1  2
.   .   .   x4x    |   8 |   4   4 |   *   * 80 |   0  0  3 |  0  0  3
-------------------+-----+---------+------------+-----------+---------
.   o3/2o3/2x .    ♦   4 |   6   0 |   4   0  0 | 160  *  * |  1  0  1
.   o3/2o   . x4*c ♦   8 |   0  12 |   0   6  0 |   * 80  * |  0  1  1
.   .   o3/2x4x4*c ♦  24 |  24  24 |   8   6  6 |   *  * 40 |  0  0  2
-------------------+-----+---------+------------+-----------+---------
o3/2o3/2o3/2x .    ♦   5 |  10   0 |  10   0  0 |   5  0  0 | 32  *  *
o3/2o3/2o   . x4*c ♦  16 |   0  32 |   0  24  0 |   0  8  0 |  * 10  *
.   o3/2o3/2x4x4*c ♦  64 |  96  96 |  64  48 24 |  16  8  8 |  *  * 10