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)
Confer
analogs:
socco series  
External
links
hedrondude

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

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