Acronym reday
Name rectified decayotton,
vertex figure of hede,
Gosset polytope 07,1
Circumradius sqrt(4/5) = 0.894427
Inradius
wrt. ene 		4/sqrt(45) = 0.596285
Inradius
wrt. rene 		1/sqrt(45) = 0.149071
Volume 251 sqrt(5)/2903040 = 0.00019333
Surface 31/2688 = 0.011533
Dihedral angles
(at margins)
  • at oca between ene and rene:   arccos(-1/9) = 96.379370°
  • at roc between rene and rene:   arccos(1/9) = 83.620630°
Face vector 45, 360, 960, 1470, 1512, 1050, 480, 135, 20
Confer
general polytopal classes:
Wythoffian polyyotta   segmentoyotta   fundamental lace prisms   Coxeter-Elte-Gosset polytopes  
analogs:
rectified simplex rSn  
External
links 		wikipedia   polytopewiki

Incidence matrix according to Dynkin symbol

o3x3o3o3o3o3o3o3o

. . . . . . . . . | 45 ♦  16 |   8  56 |  28  112 |  56  140 |  70 112 |  56  56 | 28 16 |  8  2
------------------+----+-----+---------+----------+----------+---------+---------+-------+------
. x . . . . . . . |  2 | 360 |   1   7 |   7   21 |  21   35 |  35  35 |  35  21 | 21  7 |  7  1
------------------+----+-----+---------+----------+----------+---------+---------+-------+------
o3x . . . . . . . |  3 |   3 | 120   * ♦   7    0 |  21    0 |  35   0 |  35   0 | 21  0 |  7  0
. x3o . . . . . . |  3 |   3 |   * 840 |   1    6 |   6   15 |  15  20 |  20  15 | 15  6 |  6  1
------------------+----+-----+---------+----------+----------+---------+---------+-------+------
o3x3o . . . . . . ♦  6 |  12 |   4   4 | 210    * ♦   6    0 |  15   0 |  20   0 | 15  0 |  6  0
. x3o3o . . . . . ♦  4 |   6 |   0   4 |   * 1260 |   1    5 |   5  10 |  10  10 | 10  5 |  5  1
------------------+----+-----+---------+----------+----------+---------+---------+-------+------
o3x3o3o . . . . . ♦ 10 |  30 |  10  20 |   5    5 | 252    * ♦   5   0 |  10   0 | 10  0 |  5  0
. x3o3o3o . . . . ♦  5 |  10 |   0  10 |   0    5 |   * 1260 |   1   4 |   4   6 |  6  4 |  4  1
------------------+----+-----+---------+----------+----------+---------+---------+-------+------
o3x3o3o3o . . . . ♦ 15 |  60 |  20  60 |  15   30 |   6    6 | 210   * ♦   4   0 |  6  0 |  4  0
. x3o3o3o3o . . . ♦  6 |  15 |   0  20 |   0   15 |   0    6 |   * 840 |   1   3 |  3  3 |  3  1
------------------+----+-----+---------+----------+----------+---------+---------+-------+------
o3x3o3o3o3o . . . ♦ 21 | 105 |  35 140 |  35  105 |  21   42 |   7   7 | 120   * |  3  0 |  3  0
. x3o3o3o3o3o . . ♦  7 |  21 |   0  35 |   0   35 |   0   21 |   0   7 |   * 360 |  1  2 |  2  1
------------------+----+-----+---------+----------+----------+---------+---------+-------+------
o3x3o3o3o3o3o . . ♦ 28 | 168 |  56 280 |  70  280 |  56  168 |  28  56 |   8   8 | 45  * |  2  0
. x3o3o3o3o3o3o . ♦  8 |  28 |   0  56 |   0   70 |   0   56 |   0  28 |   0   8 |  * 90 |  1  1
------------------+----+-----+---------+----------+----------+---------+---------+-------+------
o3x3o3o3o3o3o3o . ♦ 36 | 252 |  84 504 | 126  630 | 126  504 |  84 252 |  36  72 |  9  9 | 10  *
. x3o3o3o3o3o3o3o ♦  9 |  36 |   0  84 |   0  126 |   0  126 |   0  84 |   0  36 |  0  9 |  * 10


xo3ox3oo3oo3oo3oo3oo3oo&#x   → height = sqrt(5)/3 = 0.745356
(ene || rene)

o.3o.3o.3o.3o.3o.3o.3o.    | 9  * ♦  8  8   0 | 28  8  28  0   0 |  56 28  56   0   0 |  70  56  70   0   0 | 56  70  56  0   0 | 28 56  28  0  0 | 8 28  8 0 0 | 1 8 1 0
.o3.o3.o3.o3.o3.o3.o3.o    | * 36 ♦  0  2  14 |  0  1  14  7  42 |   0  7  42  21  70 |   0  21  70  35  70 |  0  35  70 35  42 |  0 35  42 21 14 | 0 21 14 7 2 | 0 7 2 1
---------------------------+------+-----------+------------------+--------------------+---------------------+-------------------+-----------------+-------------+--------
x. .. .. .. .. .. .. ..    | 2  0 | 36  *   * |  7  1   0  0   0 |  21  7   0   0   0 |  35  21   0   0   0 | 35  35   0  0   0 | 21 35   0  0  0 | 7 21  0 0 0 | 1 7 0 0
oo3oo3oo3oo3oo3oo3oo3oo&#x | 1  1 |  * 72   * |  0  1   7  0   0 |   0  7  21   0   0 |   0  21  35   0   0 |  0  35  35  0   0 |  0 35  21  0  0 | 0 21  7 0 0 | 0 7 1 0
.. .x .. .. .. .. .. ..    | 0  2 |  *  * 252 |  0  0   1  1   6 |   0  1   6   6  15 |   0   6  15  15  20 |  0  15  20 20  15 |  0 20  15 15  6 | 0 15  6 6 1 | 0 6 1 1
---------------------------+------+-----------+------------------+--------------------+---------------------+-------------------+-----------------+-------------+--------
x.3o. .. .. .. .. .. ..    | 3  0 |  3  0   0 | 84  *   *  *   * |   6  1   0   0   0 |  15   6   0   0   0 | 20  15   0  0   0 | 15 20   0  0  0 | 6 15  0 0 0 | 1 6 0 0
xo .. .. .. .. .. .. ..&#x | 2  1 |  1  2   0 |  * 36   *  *   * ♦   0  7   0   0   0 |   0  21   0   0   0 |  0  35   0  0   0 |  0 35   0  0  0 | 0 21  0 0 0 | 0 7 0 0
.. ox .. .. .. .. .. ..&#x | 1  2 |  0  2   1 |  *  * 252  *   * |   0  1   6   0   0 |   0   6  15   0   0 |  0  15  20  0   0 |  0 20  15  0  0 | 0 15  6 0 0 | 0 6 1 0
.o3.x .. .. .. .. .. ..    | 0  3 |  0  0   3 |  *  *   * 84   * ♦   0  1   0   6   0 |   0   6   0  15   0 |  0  15   0 20   0 |  0 20   0 15  0 | 0 15  0 6 0 | 0 6 0 1
.. .x3.o .. .. .. .. ..    | 0  3 |  0  0   3 |  *  *   *  * 504 |   0  0   1   1   5 |   0   1   5   5  10 |  0   5  10 10  10 |  0 10  10 10  5 | 0 10  5 5 1 | 0 5 1 1
---------------------------+------+-----------+------------------+--------------------+---------------------+-------------------+-----------------+-------------+--------
x.3o.3o. .. .. .. .. ..    ♦ 4  0 |  6  0   0 |  4  0   0  0   0 | 126  *   *   *   * |   5   1   0   0   0 | 10   5   0  0   0 | 10 10   0  0  0 | 5 10  0 0 0 | 1 5 0 0
xo3ox .. .. .. .. .. ..&#x ♦ 3  3 |  3  6   3 |  1  3   3  1   0 |   * 84   *   *   * ♦   0   6   0   0   0 |  0  15   0  0   0 |  0 20   0  0  0 | 0 15  0 0 0 | 0 6 0 0
.. ox3oo .. .. .. .. ..&#x ♦ 1  3 |  0  3   3 |  0  0   3  0   1 |   *  * 504   *   * |   0   1   5   0   0 |  0   5  10  0   0 |  0 10  10  0  0 | 0 10  5 0 0 | 0 5 1 0
.o3.x3.o .. .. .. .. ..    ♦ 0  6 |  0  0  12 |  0  0   0  4   4 |   *  *   * 126   * ♦   0   1   0   5   0 |  0   5   0 10   0 |  0 10   0 10  0 | 0 10  0 5 0 | 0 5 0 1
.. .x3.o3.o .. .. .. ..    ♦ 0  4 |  0  0   6 |  0  0   0  0   4 |   *  *   *   * 630 |   0   0   1   1   4 |  0   1   4  4   6 |  0  4   6  6  4 | 0  6  4 4 1 | 0 4 1 1
---------------------------+------+-----------+------------------+--------------------+---------------------+-------------------+-----------------+-------------+--------
x.3o.3o.3o. .. .. .. ..    ♦ 5  0 | 10  0   0 | 10  0   0  0   0 |   5  0   0   0   0 | 126   *   *   *   * |  4   1   0  0   0 |  6  4   0  0  0 | 4  6  0 0 0 | 1 4 0 0
xo3ox3oo .. .. .. .. ..&#x ♦ 4  6 |  6 12  12 |  4  6  12  4   4 |   1  4   4   1   0 |   * 126   *   *   * ♦  0   5   0  0   0 |  0 10   0  0  0 | 0 10  0 0 0 | 0 5 0 0
.. ox3oo3oo .. .. .. ..&#x ♦ 1  4 |  0  4   6 |  0  0   6  0   4 |   0  0   4   0   1 |   *   * 630   *   * |  0   1   4  0   0 |  0  4   6  0  0 | 0  6  4 0 0 | 0 4 1 0
.o3.x3.o3.o .. .. .. ..    ♦ 0 10 |  0  0  30 |  0  0   0 10  20 |   0  0   0   5   5 |   *   *   * 126   * ♦  0   1   0  4   0 |  0  4   0  6  0 | 0  6  0 4 0 | 0 4 0 1
.. .x3.o3.o3.o .. .. ..    ♦ 0  5 |  0  0  10 |  0  0   0  0  10 |   0  0   0   0   5 |   *   *   *   * 504 |  0   0   1  1   3 |  0  1   3  3  3 | 0  3  3 3 1 | 0 3 1 1
---------------------------+------+-----------+------------------+--------------------+---------------------+-------------------+-----------------+-------------+--------
x.3o.3o.3o.3o. .. .. ..    ♦ 6  0 | 15  0   0 | 20  0   0  0   0 |  15  0   0   0   0 |   6   0   0   0   0 | 84   *   *  *   * |  3  1   0  0  0 | 3  3  0 0 0 | 1 3 0 0
xo3ox3oo3oo .. .. .. ..&#x ♦ 5 10 | 10 20  30 | 10 10  30 10  20 |   5 10  20   5   5 |   1   5   5   1   0 |  * 126   *  *   * ♦  0  4   0  0  0 | 0  6  0 0 0 | 0 4 0 0
.. ox3oo3oo3oo .. .. ..&#x ♦ 1  5 |  0  5  10 |  0  0  10  0  10 |   0  0  10   0   5 |   0   0   5   0   1 |  *   * 504  *   * |  0  1   3  0  0 | 0  3  3 0 0 | 0 3 1 0
.o3.x3.o3.o3.o .. .. ..    ♦ 0 15 |  0  0  60 |  0  0   0 20  60 |   0  0   0  15  30 |   0   0   0   6   6 |  *   *   * 84   * ♦  0  1   0  3  0 | 0  3  0 3 0 | 0 3 0 1
.. .x3.o3.o3.o3.o .. ..    ♦ 0  6 |  0  0  15 |  0  0   0  0  20 |   0  0   0   0  15 |   0   0   0   0   6 |  *   *   *  * 252 |  0  0   1  1  2 | 0  1  2 2 1 | 0 2 1 1
---------------------------+------+-----------+------------------+--------------------+---------------------+-------------------+-----------------+-------------+--------
x.3o.3o.3o.3o.3o. .. ..    ♦ 7  0 | 21  0   0 | 35  0   0  0   0 |  35  0   0   0   0 |  21   0   0   0   0 |  7   0   0  0   0 | 36  *   *  *  * | 2  1  0 0 0 | 1 2 0 0
xo3ox3oo3oo3oo .. .. ..&#x ♦ 6 15 | 15 30  60 | 20 15  60 20  60 |  15 20  60  15  30 |   6  15  30   6   6 |  1   6   6  1   0 |  * 84   *  *  * | 0  3  0 0 0 | 0 3 0 0
.. ox3oo3oo3oo3oo .. ..&#x ♦ 1  6 |  0  6  15 |  0  0  15  0  20 |   0  0  20   0  15 |   0   0  15   0   6 |  0   0   6  0   1 |  *  * 252  *  * | 0  1  2 0 0 | 0 2 1 0
.o3.x3.o3.o3.o3.o .. ..    ♦ 0 21 |  0  0 105 |  0  0   0 35 140 |   0  0   0  35 105 |   0   0   0  21  42 |  0   0   0  7   7 |  *  *   * 36  * | 0  1  0 2 0 | 0 2 0 1
.. .x3.o3.o3.o3.o3.o ..    ♦ 0  7 |  0  0  21 |  0  0   0  0  35 |   0  0   0   0  35 |   0   0   0   0  21 |  0   0   0  0   7 |  *  *   *  * 72 | 0  0  1 1 1 | 0 1 1 1
---------------------------+------+-----------+------------------+--------------------+---------------------+-------------------+-----------------+-------------+--------
x.3o.3o.3o.3o.3o.3o. ..    ♦ 8  0 | 28  0   0 | 56  0   0  0   0 |  70  0   0   0   0 |  56   0   0   0   0 | 28   0   0  0   0 |  8  0   0  0  0 | 9  *  * * * | 1 1 0 0
xo3ox3oo3oo3oo3oo .. ..&#x ♦ 7 21 | 21 42 105 | 35 21 105 35 140 |  35 35 140  35 105 |  21  35 105  21  42 |  7  21  42  7   7 |  1  7   7  1  0 | * 36  * * * | 0 2 0 0
.. ox3oo3oo3oo3oo3oo ..&#x ♦ 1  7 |  0  7  21 |  0  0  21  0  35 |   0  0  35   0  35 |   0   0  35   0  21 |  0   0  21  0   7 |  0  0   7  0  1 | *  * 72 * * | 0 1 1 0
.o3.x3.o3.o3.o3.o3.o ..    ♦ 0 28 |  0  0 168 |  0  0   0 56 280 |   0  0   0  70 280 |   0   0   0  56 168 |  0   0   0 28  56 |  0  0   0  8  8 | *  *  * 9 * | 0 1 0 1
.. .x3.o3.o3.o3.o3.o3.o    ♦ 0  8 |  0  0  28 |  0  0   0  0  56 |   0  0   0   0  70 |   0   0   0   0  56 |  0   0   0  0  28 |  0  0   0  0  8 | *  *  * * 9 | 0 0 1 1
---------------------------+------+-----------+------------------+--------------------+---------------------+-------------------+-----------------+-------------+--------
x.3o.3o.3o.3o.3o.3o.3o.    ♦ 9  0 | 36  0   0 | 84  0   0  0   0 | 126  0   0   0   0 | 126   0   0   0   0 | 84   0   0  0   0 | 36  0   0  0  0 | 9  0  0 0 0 | 1 * * *
xo3ox3oo3oo3oo3oo3oo ..&#x ♦ 8 28 | 28 56 168 | 56 28 168 56 280 |  70 56 280  70 280 |  56  70 280  56 168 | 28  56 168 28  56 |  8 28  56  8  8 | 1  8  8 1 0 | * 9 * *
.. ox3oo3oo3oo3oo3oo3oo&#x ♦ 1  8 |  0  8  28 |  0  0  28  0  56 |   0  0  56   0  70 |   0   0  70   0  56 |  0   0  56  0  28 |  0  0  28  0  8 | 0  0  8 0 1 | * * 9 *
.o3.x3.o3.o3.o3.o3.o3.o    ♦ 0 36 |  0  0 252 |  0  0   0 84 504 |   0  0   0 126 630 |   0   0   0 126 504 |  0   0   0 84 252 |  0  0   0 36 72 | 0  0  0 9 9 | * * * 1

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