Acronym	day
Name	decayotton, 9D simplex (α9), pyroxenn(id), enneazettal pyramid, vertex figure of ux, Gosset polytope 08
Circumradius	sqrt(9/20) = 0.670820
Inradius	1/sqrt(180) = 0.074536
Volume	sqrt(5)/5806080 = 0.00000038513
Surface	1/21504 = 0.000046503
Dual	(selfdual, in different orientation)
Dihedral angles (at margins)	at oca between ene and ene:   arccos(1/9) = 83.620630°
Face vector	10, 45, 120, 210, 252, 210, 120, 45, 10
Confer	general polytopal classes: Wythoffian polyyotta   simplex   noble polytopes   segmentoyotta   fundamental lace prisms   Coxeter-Elte-Gosset polytopes   analogs: regular simplex Sn
External links

Incidence matrix according to Dynkin symbol

x3o3o3o3o3o3o3o3o

. . . . . . . . . | 10 ♦  9 |  36 |  84 | 126 | 126 |  84 | 36 |  9
------------------+----+----+-----+-----+-----+-----+-----+----+---
x . . . . . . . . |  2 | 45 ♦   8 |  28 |  56 |  70 |  56 | 28 |  8
------------------+----+----+-----+-----+-----+-----+-----+----+---
x3o . . . . . . . |  3 |  3 | 120 ♦   7 |  21 |  35 |  35 | 21 |  7
------------------+----+----+-----+-----+-----+-----+-----+----+---
x3o3o . . . . . . ♦  4 |  6 |   4 | 210 ♦   6 |  15 |  20 | 15 |  6
------------------+----+----+-----+-----+-----+-----+-----+----+---
x3o3o3o . . . . . ♦  5 | 10 |  10 |   5 | 252 ♦   5 |  10 | 10 |  5
------------------+----+----+-----+-----+-----+-----+-----+----+---
x3o3o3o3o . . . . ♦  6 | 15 |  20 |  15 |   6 | 210 ♦   4 |  6 |  4
------------------+----+----+-----+-----+-----+-----+-----+----+---
x3o3o3o3o3o . . . ♦  7 | 21 |  35 |  35 |  21 |   7 | 120 |  3 |  3
------------------+----+----+-----+-----+-----+-----+-----+----+---
x3o3o3o3o3o3o . . ♦  8 | 28 |  56 |  70 |  56 |  28 |   8 | 45 |  2
------------------+----+----+-----+-----+-----+-----+-----+----+---
x3o3o3o3o3o3o3o . ♦  9 | 36 |  84 | 126 | 126 |  84 |  36 |  9 | 10

ox3oo3oo3oo3oo3oo3oo3oo&#x   → height = sqrt(5)/3 = 0.745356
(point || ene)

o.3o.3o.3o.3o.3o.3o.3o.    | 1 * ♦ 9  0 | 36  0 | 84   0 | 126   0 | 126  0 | 84  0 | 36 0 | 9 0
.o3.o3.o3.o3.o3.o3.o3.o    | * 9 ♦ 1  8 |  8 28 | 28  56 |  56  70 |  70 56 | 56 28 | 28 8 | 8 1
---------------------------+-----+------+-------+--------+---------+--------+-------+------+----
oo3oo3oo3oo3oo3oo3oo3oo&#x | 1 1 | 9  * ♦  8  0 | 28   0 |  56   0 |  70  0 | 56  0 | 28 0 | 8 0
.x .. .. .. .. .. .. ..    | 0 2 | * 36 ♦  1  7 |  7  21 |  21  35 |  35 35 | 35 21 | 21 7 | 7 1
---------------------------+-----+------+-------+--------+---------+--------+-------+------+----
ox .. .. .. .. .. .. ..&#x | 1 2 | 2  1 | 36  * ♦  7   0 |  21   0 |  35  0 | 35  0 | 21 0 | 7 0
.x3.o .. .. .. .. .. ..    | 0 3 | 0  3 |  * 84 ♦  1   6 |   6  15 |  15 20 | 20 15 | 15 6 | 6 1
---------------------------+-----+------+-------+--------+---------+--------+-------+------+----
ox3oo .. .. .. .. .. ..&#x ♦ 1 3 | 3  3 |  3  1 | 84   * ♦   6   0 |  15  0 | 20  0 | 15 0 | 6 0
.x3.o3.o .. .. .. .. ..    ♦ 0 4 | 0  6 |  0  4 |  * 126 ♦   1   5 |   5 10 | 10 10 | 10 5 | 5 1
---------------------------+-----+------+-------+--------+---------+--------+-------+------+----
ox3oo3oo .. .. .. .. ..&#x ♦ 1 4 | 4  6 |  6  4 |  4   1 | 126   * ♦   5  0 | 10  0 | 10 0 | 5 0
.x3.o3.o3.o .. .. .. ..    ♦ 0 5 | 0 10 |  0 10 |  0   5 |   * 126 ♦   1  4 |  4  6 |  6 4 | 4 1
---------------------------+-----+------+-------+--------+---------+--------+-------+------+----
ox3oo3oo3oo .. .. .. ..&#x ♦ 1 5 | 5 10 | 10 10 | 10   5 |   5   1 | 126  * ♦  4  0 |  6 0 | 4 0
.x3.o3.o3.o3.o .. .. ..    ♦ 0 6 | 0 15 |  0 20 |  0  15 |   0   6 |   * 84 ♦  1  3 |  3 3 | 3 1
---------------------------+-----+------+-------+--------+---------+--------+-------+------+----
ox3oo3oo3oo3oo .. .. ..&#x ♦ 1 6 | 6 15 | 15 20 | 20  15 |  15   6 |   6  1 | 84  * |  3 0 | 3 0
.x3.o3.o3.o3.o3.o .. ..    ♦ 0 7 | 0 21 |  0 35 |  0  35 |   0  21 |   0  7 |  * 36 |  1 2 | 2 1
---------------------------+-----+------+-------+--------+---------+--------+-------+------+----
ox3oo3oo3oo3oo3oo .. ..&#x ♦ 1 7 | 7 21 | 21 35 | 35  35 |  35  21 |  21  7 |  7  1 | 36 * | 2 0
.x3.o3.o3.o3.o3.o3.o ..    ♦ 0 8 | 0 28 |  0 56 |  0  70 |   0  56 |   0 28 |  0  8 |  * 9 | 1 1
---------------------------+-----+------+-------+--------+---------+--------+-------+------+----
ox3oo3oo3oo3oo3oo3oo ..&#x ♦ 1 8 | 8 28 | 28 56 | 56  70 |  70  56 |  56 28 | 28  8 |  8 1 | 9 *
.x3.o3.o3.o3.o3.o3.o3.o    ♦ 0 9 | 0 36 |  0 84 |  0 126 |   0 126 |   0 84 |  0 36 |  0 9 | * 1