Acronym	deker
Name	dekeract, icosaxennon, 10D measure-polytope (γ10), geodak(id)
Circumradius	sqrt(5/2) = 1.581139
Inradius	1/2
Vertex layers	Layer Symmetry Subsymmetries   o3o3o3o3o3o3o3o3o4o o3o3o3o3o3o3o3o3o . . o3o3o3o3o3o3o3o4o 1 o3o3o3o3o3o3o3o3o4x o3o3o3o3o3o3o3o3o . vertex first . o3o3o3o3o3o3o3o4x enne first 2 o3o3o3o3o3o3o3o3q . vertex figure . o3o3o3o3o3o3o3o4x opposite enne 3 o3o3o3o3o3o3o3q3o .   4 o3o3o3o3o3o3q3o3o . 5 o3o3o3o3o3q3o3o3o . 6 o3o3o3o3q3o3o3o3o . 7 o3o3o3q3o3o3o3o3o . 8 o3o3q3o3o3o3o3o3o . 9 o3q3o3o3o3o3o3o3o . 10 q3o3o3o3o3o3o3o3o . 11 o3o3o3o3o3o3o3o3o . opposite vertex
Coordinates	(1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2)   & all changes of sign
Volume	1
Surface	20
Dual	ka
Dihedral angles (at margins)	at octo between enne and enne:   90°
Face vector	1024, 5120, 11520, 15360, 13440, 8064, 3360, 960, 180, 20
Confer	general polytopal classes: Wythoffian polyxenna   hypercube   analogs: regular hypercube Cn
External links

Incidence matrix according to Dynkin symbol

o3o3o3o3o3o3o3o3o4x

. . . . . . . . . . | 1024 ♦   10 |    45 |   120 |   210 |  252 |  210 | 120 |  45 | 10
--------------------+------+------+-------+-------+-------+------+------+-----+-----+---
. . . . . . . . . x |    2 | 5120 ♦     9 |    36 |    84 |  126 |  126 |  84 |  36 |  9
--------------------+------+------+-------+-------+-------+------+------+-----+-----+---
. . . . . . . . o4x |    4 |    4 | 11520 ♦     8 |    28 |   56 |   70 |  56 |  28 |  8
--------------------+------+------+-------+-------+-------+------+------+-----+-----+---
. . . . . . . o3o4x ♦    8 |   12 |     6 | 15360 ♦     7 |   21 |   35 |  35 |  21 |  7
--------------------+------+------+-------+-------+-------+------+------+-----+-----+---
. . . . . . o3o3o4x ♦   16 |   32 |    24 |     8 | 13440 ♦    6 |   15 |  20 |  15 |  6
--------------------+------+------+-------+-------+-------+------+------+-----+-----+---
. . . . . o3o3o3o4x ♦   32 |   80 |    80 |    40 |    10 | 8064 ♦    5 |  10 |  10 |  5
--------------------+------+------+-------+-------+-------+------+------+-----+-----+---
. . . . o3o3o3o3o4x ♦   64 |  192 |   240 |   160 |    60 |   12 | 3360 ♦   4 |   6 |  4
--------------------+------+------+-------+-------+-------+------+------+-----+-----+---
. . . o3o3o3o3o3o4x ♦  128 |  448 |   672 |   560 |   280 |   84 |   14 | 960 |   3 |  3
--------------------+------+------+-------+-------+-------+------+------+-----+-----+---
. . o3o3o3o3o3o3o4x ♦  256 | 1024 |  1792 |  1792 |  1120 |  448 |  112 |  16 | 180 |  2
--------------------+------+------+-------+-------+-------+------+------+-----+-----+---
. o3o3o3o3o3o3o3o4x ♦  512 | 2304 |  4608 |  5376 |  4032 | 2016 |  672 | 144 |  18 | 20

snubbed forms: o3o3o3o3o3o3o3o3o4s