Acronym renepy
Name rectified-enneazettonal pyramid,
vertex pyramid of demienneract
Circumradius 3/sqrt(8) = 1.060660
Inradius
wrt. ene
7/sqrt(72) = 0.824958
Inradius
wrt. rocpy
1/sqrt(8) = 0.353553
Inradius
wrt. rene
-5/sqrt(72) = -0.589256
Volume 247 sqrt(2)/5806080 = 0.000060163
Dihedral angles
(at margins)
Face vector 37, 288, 840, 1344, 1386, 966, 444, 126, 19
Confer
uniform relative:
henne  
general polytopal classes:
segmentoyotta   fundamental lace prisms  
analogs:
rectified simplex pyramid rSn-py  

Incidence matrix according to Dynkin symbol

oo3ox3oo3oo3oo3oo3oo3oo&#x   → height = sqrt(2)/3 = 0.471405
(pt || rene)

o.3o.3o.3o.3o.3o.3o.3o.    | 1  *  36   0 | 252  0   0 | 84 504   0   0 | 126 630   0   0 | 126 504  0   0 | 84 252  0  0 | 36 72 0 0 | 9 9 0
.o3.o3.o3.o3.o3.o3.o3.o    | * 36 |  1  14 |  14  7  42 |  7  42  21  70 |  21  70  35  70 |  35  70 35  42 | 35  42 21 14 | 21 14 7 2 | 7 2 1
---------------------------+------+--------+------------+----------------+-----------------+----------------+--------------+-----------+------
oo3oo3oo3oo3oo3oo3oo3oo&#x | 1  1 | 36   *   14  0   0 |  7  42   0   0 |  21  70   0   0 |  35  70  0   0 | 35  42  0  0 | 21 14 0 0 | 7 2 0
.. .x .. .. .. .. .. ..    | 0  2 |  * 252 |   1  1   6 |  1   6   6  15 |   6  15  15  20 |  15  20 20  15 | 20  15 15  6 | 15  6 6 1 | 6 1 1
---------------------------+------+--------+------------+----------------+-----------------+----------------+--------------+-----------+------
.. ox .. .. .. .. .. ..&#x | 1  2 |  2   1 | 252  *   * |  1   6   0   0 |   6  15   0   0 |  15  20  0   0 | 20  15  0  0 | 15  6 0 0 | 6 1 0
.o3.x .. .. .. .. .. ..    | 0  3 |  0   3 |   * 84   * |  1   0   6   0 |   6   0  15   0 |  15   0 20   0 | 20   0 15  0 | 15  0 6 0 | 6 0 1
.. .x3.o .. .. .. .. ..    | 0  3 |  0   3 |   *  * 504 |  0   1   1   5 |   1   5   5  10 |   5  10 10  10 | 10  10 10  5 | 10  5 5 1 | 5 1 1
---------------------------+------+--------+------------+----------------+-----------------+----------------+--------------+-----------+------
oo3ox .. .. .. .. .. ..&#x  1  3 |  3   3 |   3  1   0 | 84   *   *   *    6   0   0   0 |  15   0  0   0 | 20   0  0  0 | 15  0 0 0 | 6 0 0
.. ox3oo .. .. .. .. ..&#x  1  3 |  3   3 |   3  0   1 |  * 504   *   * |   1   5   0   0 |   5  10  0   0 | 10  10  0  0 | 10  5 0 0 | 5 1 0
.o3.x3.o .. .. .. .. ..     0  6 |  0  12 |   0  4   4 |  *   * 126   * |   1   0   5   0 |   5   0 10   0 | 10   0 10  0 | 10  0 5 0 | 5 0 1
.. .x3.o3.o .. .. .. ..     0  4 |  0   6 |   0  0   4 |  *   *   * 630 |   0   1   1   4 |   1   4  4   6 |  4   6  6  4 |  6  4 4 1 | 4 1 1
---------------------------+------+--------+------------+----------------+-----------------+----------------+--------------+-----------+------
oo3ox3oo .. .. .. .. ..&#x  1  6 |  6  12 |  12  4   4 |  4   4   1   0 | 126   *   *   *    5   0  0   0 | 10   0  0  0 | 10  0 0 0 | 5 0 0
.. ox3oo3oo .. .. .. ..&#x  1  4 |  4   6 |   6  0   4 |  0   4   0   1 |   * 630   *   * |   1   4  0   0 |  4   6  0  0 |  6  4 0 0 | 4 1 0
.o3.x3.o3.o .. .. .. ..     0 10 |  0  30 |   0 10  20 |  0   0   5   5 |   *   * 126   * |   1   0  4   0 |  4   0  6  0 |  6  0 4 0 | 4 0 1
.. .x3.o3.o3.o .. .. ..     0  5 |  0  10 |   0  0  10 |  0   0   0   5 |   *   *   * 504 |   0   1  1   3 |  1   3  3  3 |  3  3 3 1 | 3 1 1
---------------------------+------+--------+------------+----------------+-----------------+----------------+--------------+-----------+------
oo3ox3oo3oo .. .. .. ..&#x  1 10 | 10  30 |  30 10  20 | 10  20   5   5 |   5   5   1   0 | 126   *  *   *   4   0  0  0 |  6  0 0 0 | 4 0 0
.. ox3oo3oo3oo .. .. ..&#x  1  5 |  5  10 |  10  0  10 |  0  10   0   5 |   0   5   0   1 |   * 504  *   * |  1   3  0  0 |  3  3 0 0 | 3 1 0
.o3.x3.o3.o3.o .. .. ..     0 15 |  0  60 |   0 20  60 |  0   0  15  30 |   0   0   6   6 |   *   * 84   * |  1   0  3  0 |  3  0 3 0 | 3 0 1
.. .x3.o3.o3.o3.o .. ..     0  6 |  0  15 |   0  0  20 |  0   0   0  15 |   0   0   0   6 |   *   *  * 252 |  0   1  1  2 |  1  2 2 1 | 2 1 1
---------------------------+------+--------+------------+----------------+-----------------+----------------+--------------+-----------+------
oo3ox3oo3oo3oo .. .. ..&#x  1 15 | 15  60 |  60 20  60 | 20  60  15  30 |  15  30   6   6 |   6   6  1   0 | 84   *  *  * |  3  0 0 0 | 3 0 0
.. ox3oo3oo3oo3oo .. ..&#x  1  6 |  6  15 |  15  0  20 |  0  20   0  15 |   0  15   0   6 |   0   6  0   1 |  * 252  *  * |  1  2 0 0 | 2 1 0
.o3.x3.o3.o3.o3.o .. ..     0 21 |  0 105 |   0 35 140 |  0   0  35 105 |   0   0  21  42 |   0   0  7   7 |  *   * 36  * |  1  0 2 0 | 2 0 1
.. .x3.o3.o3.o3.o3.o ..     0  7 |  0  21 |   0  0  35 |  0   0   0  35 |   0   0   0  21 |   0   0  0   7 |  *   *  * 72 |  0  1 1 1 | 1 1 1
---------------------------+------+--------+------------+----------------+-----------------+----------------+--------------+-----------+------
oo3ox3oo3oo3oo3oo .. ..&#x  1 21 | 21 105 | 105 35 140 | 35 140  35 105 |  35 105  21  42 |  21  42  7   7 |  7   7  1  0 | 36  * * * | 2 0 0
.. ox3oo3oo3oo3oo3oo ..&#x  1  7 |  7  21 |  21  0  35 |  0  35   0  35 |   0  35   0  21 |   0  21  0   7 |  0   7  0  1 |  * 72 * * | 1 1 0
.o3.x3.o3.o3.o3.o3.o ..     0 28 |  0 168 |   0 56 280 |  0   0  70 280 |   0   0  56 168 |   0   0 28  56 |  0   0  8  8 |  *  * 9 * | 1 0 1
.. .x3.o3.o3.o3.o3.o3.o     0  8 |  0  28 |   0  0  56 |  0   0   0  70 |   0   0   0  56 |   0   0  0  28 |  0   0  0  8 |  *  * * 9 | 0 1 1
---------------------------+------+--------+------------+----------------+-----------------+----------------+--------------+-----------+------
oo3ox3oo3oo3oo3oo3oo ..&#x  1 28 | 28 168 | 168 56 280 | 56 280  70 280 |  70 280  56 168 |  56 168 28  56 | 28  56  8  8 |  8  8 1 0 | 9 * *
.. ox3oo3oo3oo3oo3oo3oo&#x  1  8 |  8  28 |  28  0  56 |  0  56   0  70 |   0  70   0  56 |   0  56  0  28 |  0  28  0  8 |  0  8 0 1 | * 9 *
.o3.x3.o3.o3.o3.o3.o3.o     0 36 |  0 252 |   0 84 504 |  0   0 126 630 |   0   0 126 504 |   0   0 84 252 |  0   0 36 72 |  0  0 9 9 | * * 1

© 2004-2024
top of page