Acronym sinnont
Name small penteractipenteractitriacontiditeron
Field of sections
 ©
Circumradius sqrt[7+2 sqrt(2)]/2 = 1.567516
Vertex figure
 ©
Coordinates ((1+sqrt(2))/2, 1/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign
General of army scant
Colonel of regiment scant
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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