Acronym	ka
Name	chilliaicositetraxennon, decacross (β10), aerodak(id), decayottal antiprism, Gosset polytope 71,1, lattice C10 contact polytope (span of its small roots)
Circumradius	1/sqrt(2) = 0.707107
Inradius	1/sqrt(20) = 0.223607
Lace city in approx. ASCII-art	©   o -- o3o3o3o3o3o3o3o4o (point) o e o -- x3o3o3o3o3o3o3o4o (vee) o -- o3o3o3o3o3o3o3o4o (point) where: o = o3o3o3o3o3o3o4o (point) e = x3o3o3o3o3o3o4o (ek)
Coordinates	(1/sqrt(2), 0, 0, 0, 0, 0, 0, 0, 0, 0)   & all permutations, all changes of sign
Volume	1/113400 = 0.0000088183
Surface	sqrt(5)/5670 = 0.00039437
Dual	deker
Dihedral angles	at ene between day and day:   arccos(-4/5) = 143.130102°
Face vector	20, 180, 960, 3360, 8064, 13440, 15360, 11520, 5120, 1024
Confer	more general: xPo3o...o3o4o   general polytopal classes: Wythoffian polyxenna   orthoplex   segmentoxenna   fundamental lace prisms   Coxeter-Elte-Gosset polytopes   analogs: regular orthoplex On
External links

Incidence matrix according to Dynkin symbol

x3o3o3o3o3o3o3o3o4o

. . . . . . . . . . | 20 ♦  18 | 144 |  672 | 2016 |  4032 |  5376 |  4608 | 2304 |  512
--------------------+----+-----+-----+------+------+-------+-------+-------+------+-----
x . . . . . . . . . |  2 | 180 ♦  16 |  112 |  448 |  1120 |  1792 |  1792 | 1024 |  256
--------------------+----+-----+-----+------+------+-------+-------+-------+------+-----
x3o . . . . . . . . |  3 |   3 | 960 ♦   14 |   84 |   280 |   560 |   672 |  448 |  128
--------------------+----+-----+-----+------+------+-------+-------+-------+------+-----
x3o3o . . . . . . . ♦  4 |   6 |   4 | 3360 ♦   12 |    60 |   160 |   240 |  192 |   64
--------------------+----+-----+-----+------+------+-------+-------+-------+------+-----
x3o3o3o . . . . . . ♦  5 |  10 |  10 |    5 | 8064 ♦    10 |    40 |    80 |   80 |   32
--------------------+----+-----+-----+------+------+-------+-------+-------+------+-----
x3o3o3o3o . . . . . ♦  6 |  15 |  20 |   15 |    6 | 13440 ♦     8 |    24 |   32 |   16
--------------------+----+-----+-----+------+------+-------+-------+-------+------+-----
x3o3o3o3o3o . . . . ♦  7 |  21 |  35 |   35 |   21 |     7 | 15360 ♦     6 |   12 |    8
--------------------+----+-----+-----+------+------+-------+-------+-------+------+-----
x3o3o3o3o3o3o . . . ♦  8 |  28 |  56 |   70 |   56 |    28 |     8 | 11520 |    4 |    4
--------------------+----+-----+-----+------+------+-------+-------+-------+------+-----
x3o3o3o3o3o3o3o . . ♦  9 |  36 |  84 |  126 |  126 |    84 |    36 |     9 | 5120 |    2
--------------------+----+-----+-----+------+------+-------+-------+-------+------+-----
x3o3o3o3o3o3o3o3o . ♦ 10 |  45 | 120 |  210 |  252 |   210 |   120 |    45 |   10 | 1024

o3o3o *b3o3o3o3o3o3o3x

. . .    . . . . . . . | 20 ♦  18 | 114 |  672 | 2016 |  4032 |  5376 |  4608 | 2304 | 256 256
-----------------------+----+-----+-----+------+------+-------+-------+-------+------+--------
. . .    . . . . . . x |  2 | 180 ♦  16 |  112 |  448 |  1120 |  1792 |  1792 | 1024 | 128 128
-----------------------+----+-----+-----+------+------+-------+-------+-------+------+--------
. . .    . . . . . o3x |  3 |   3 | 960 ♦   14 |   84 |   280 |   560 |   672 |  448 |  64  64
-----------------------+----+-----+-----+------+------+-------+-------+-------+------+--------
. . .    . . . . o3o3x ♦  4 |   6 |   4 | 3360 ♦   12 |    60 |   160 |   240 |  192 |  32  32
-----------------------+----+-----+-----+------+------+-------+-------+-------+------+--------
. . .    . . . o3o3o3x ♦  5 |  10 |  10 |    5 | 8064 ♦    10 |    40 |    80 |   80 |  16  16
-----------------------+----+-----+-----+------+------+-------+-------+-------+------+--------
. . .    . . o3o3o3o3x ♦  6 |  15 |  20 |   15 |    6 | 13440 ♦     8 |    24 |   32 |   8   8
-----------------------+----+-----+-----+------+------+-------+-------+-------+------+--------
. . .    . o3o3o3o3o3x ♦  7 |  21 |  35 |   35 |   21 |     7 | 15360 ♦     6 |   12 |   4   4
-----------------------+----+-----+-----+------+------+-------+-------+-------+------+--------
. . .    o3o3o3o3o3o3x ♦  8 |  28 |  56 |   70 |   56 |    28 |     8 | 11520 |    4 |   2   2
-----------------------+----+-----+-----+------+------+-------+-------+-------+------+--------
. o . *b3o3o3o3o3o3o3x ♦  9 |  36 |  84 |  126 |  126 |    84 |    36 |     9 | 5120 |   1   1
-----------------------+----+-----+-----+------+------+-------+-------+-------+------+--------
o3o . *b3o3o3o3o3o3o3x ♦ 10 |  45 | 120 |  210 |  252 |   210 |   120 |    45 |   10 | 512   *
. o3o *b3o3o3o3o3o3o3x ♦ 10 |  45 | 120 |  210 |  252 |   210 |   120 |    45 |   10 |   * 512