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

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