Acronym he (old: ache)
Name hexadecaexon,
trirectified octaexon,
equatorial cross-section of (vertex first) 1/q-octo,
Gosset polytope 03,3
Circumradius 1
Inradius 1/sqrt(7) = 0.377964
Lace city
in approx. ASCII-art
R   D 		R = o3x3o3o3o (rix)
      		D = o3o3x3o3o (dot)
 D   r		r = o3o3o3x3o
Dihedral angles
(at margins)
  • at dot between bril and bril:   arccos(-1/7) = 98.213211°
  • at rix between bril and bril:   arccos(1/7) = 81.786789°
Confer
related segmentoexa:
tetdippy  
general polytopal classes:
noble polytopes   segmentoexa   fundamental lace prisms   Coxeter-Elte-Gosset polytopes  
External
links
wikipedia  

Incidence matrix according to Dynkin symbol

o3o3o3x3o3o3o

. . . . . . . | 70   16 |  24  24 |  16  36  16 |  4  24  24  4 |  6 16  6 | 4 4
--------------+----+-----+---------+-------------+---------------+----------+----
. . . x . . . |  2 | 560 |   3   3 |   3   9   3 |  1   9   9  1 |  3  9  3 | 3 3
--------------+----+-----+---------+-------------+---------------+----------+----
. . o3x . . . |  3 |   3 | 560   * |   2   3   0 |  1   6   3  0 |  3  6  1 | 3 2
. . . x3o . . |  3 |   3 |   * 560 |   0   3   2 |  0   3   6  1 |  1  6  3 | 2 3
--------------+----+-----+---------+-------------+---------------+----------+----
. o3o3x . . .   4 |   6 |   4   0 | 280   *   * |  1   3   0  0 |  3  3  0 | 3 1
. . o3x3o . .   6 |  12 |   4   4 |   * 420   * |  0   2   2  0 |  1  4  1 | 2 2
. . . x3o3o .   4 |   6 |   0   4 |   *   * 280 |  0   0   3  1 |  0  3  3 | 1 3
--------------+----+-----+---------+-------------+---------------+----------+----
o3o3o3x . . .   5 |  10 |  10   0 |   5   0   0 | 56   *   *  * |  3  0  0 | 3 0
. o3o3x3o . .  10 |  30 |  20  10 |   5   5   0 |  * 168   *  * |  1  2  0 | 2 1
. . o3x3o3o .  10 |  30 |  10  20 |   0   5   5 |  *   * 168  * |  0  2  1 | 1 2
. . . x3o3o3o   5 |  10 |   0  10 |   0   0   5 |  *   *   * 56 |  0  0  3 | 0 3
--------------+----+-----+---------+-------------+---------------+----------+----
o3o3o3x3o . .  15 |  60 |  60  20 |  30  15   0 |  6   6   0  0 | 28  *  * | 2 0
. o3o3x3o3o .  20 |  90 |  60  60 |  15  30  15 |  0   6   6  0 |  * 56  * | 1 1
. . o3x3o3o3o  15 |  60 |  20  60 |   0  15  30 |  0   0   6  6 |  *  * 28 | 0 2
--------------+----+-----+---------+-------------+---------------+----------+----
o3o3o3x3o3o .  35 | 210 | 210 140 | 105 105  35 | 21  42  21  0 |  7  7  0 | 8 *
. o3o3x3o3o3o  35 | 210 | 140 210 |  35 105 105 |  0  21  42 21 |  0  7  7 | * 8
or
. . . . . . .    | 70   16 |   48 |  32  36 |   8  48 | 12 16 |  8
-----------------+----+-----+------+---------+---------+-------+---
. . . x . . .    |  2 | 560 |    6 |   6   9 |   2  18 |  6  9 |  6
-----------------+----+-----+------+---------+---------+-------+---
. . o3x . . .  & |  3 |   3 | 1120 |   2   3 |   1   9 |  4  6 |  5
-----------------+----+-----+------+---------+---------+-------+---
. o3o3x . . .  &   4 |   6 |    4 | 560   * |   1   3 |  3  3 |  4
. . o3x3o . .      6 |  12 |    8 |   * 420 |   0   4 |  2  4 |  4
-----------------+----+-----+------+---------+---------+-------+---
o3o3o3x . . .  &   5 |  10 |   10 |   5   0 | 112   * |  3  0 |  3
. o3o3x3o . .  &  10 |  30 |   30 |   5   5 |   * 336 |  1  2 |  3
-----------------+----+-----+------+---------+---------+-------+---
o3o3o3x3o . .  &  15 |  60 |   80 |  30  15 |   6   6 | 56  * |  2
. o3o3x3o3o .     20 |  90 |  120 |  30  30 |   0  12 |  * 56 |  2
-----------------+----+-----+------+---------+---------+-------+---
o3o3o3x3o3o .  &  35 | 210 |  350 | 140 105 |  21  63 |  7  7 | 16

oo3oo3xo3ox3oo3oo&#x   → height = 2/sqrt(7) = 0.755929
(bril || inv bril)

o.3o.3o.3o.3o.3o.    | 35  *   12   4   0 |  12  18  12   6   0   0 |  4  18  12  12  18   4   0   0  0 |  6 12  3  4  18  12  1  0  0  0 | 4 3  6 12  3 0 0 | 1 4 3 0
.o3.o3.o3.o3.o3.o    |  * 35    0   4  12 |   0   0   6  12  18  12 |  0   0   0   4  18  12  12  18  4 |  0  0  0  1  12  18  4  3 12  6 | 0 0  3 12  6 3 4 | 0 3 4 1
---------------------+-------+-------------+-------------------------+-----------------------------------+---------------------------------+------------------+--------
.. .. x. .. .. ..    |  2  0 | 210   *   * |   2   3   1   0   0   0 |  1   6   3   2   3   0   0   0  0 |  3  6  1  1   6   3  0  0  0  0 | 3 2  3  6  1 0 0 | 1 3 2 0
oo3oo3oo3oo3oo3oo&#x |  1  1 |   * 140   * |   0   0   3   3   0   0 |  0   0   0   3   9   3   0   0  0 |  0  0  0  1   9   9  1  0  0  0 | 0 0  3  9  3 0 0 | 0 3 3 0
.. .. .. .x .. ..    |  0  2 |   *   * 210 |   0   0   0   1   3   2 |  0   0   0   0   3   2   3   6  1 |  0  0  0  0   3   6  1  1  6  3 | 0 0  1  6  3 2 3 | 0 2 3 1
---------------------+-------+-------------+-------------------------+-----------------------------------+---------------------------------+------------------+--------
.. o.3x. .. .. ..    |  3  0 |   3   0   0 | 140   *   *   *   *   * |  1   3   0   1   0   0   0   0  0 |  3  3  0  1   3   0  0  0  0  0 | 3 1  3  3  0 0 0 | 1 3 1 0
.. .. x.3o. .. ..    |  3  0 |   3   0   0 |   * 210   *   *   *   * |  0   2   2   0   1   0   0   0  0 |  1  4  1  0   2   2  0  0  0  0 | 2 2  1  4  1 0 0 | 1 2 2 0
.. .. xo .. .. ..&#x |  2  1 |   1   2   0 |   *   * 210   *   *   * |  0   0   0   2   3   0   0   0  0 |  0  0  0  1   6   3  0  0  0  0 | 0 0  3  6  1 0 0 | 0 3 2 0
.. .. .. ox .. ..&#x |  1  2 |   0   2   1 |   *   *   * 210   *   * |  0   0   0   0   3   2   0   0  0 |  0  0  0  0   3   6  1  0  0  0 | 0 0  1  6  3 0 0 | 0 2 3 0
.. .. .o3.x .. ..    |  0  3 |   0   0   3 |   *   *   *   * 210   * |  0   0   0   0   1   0   2   2  0 |  0  0  0  0   2   2  0  1  4  1 | 0 0  1  4  1 2 2 | 0 2 2 1
.. .. .. .x3.o ..    |  0  3 |   0   0   3 |   *   *   *   *   * 140 |  0   0   0   0   0   1   0   3  1 |  0  0  0  0   0   3  1  0  3  3 | 0 0  0  3  3 1 3 | 0 1 3 1
---------------------+-------+-------------+-------------------------+-----------------------------------+---------------------------------+------------------+--------
o.3o.3x. .. .. ..      4  0 |   6   0   0 |   4   0   0   0   0   0 | 35   *   *   *   *   *   *   *  * |  3  0  0  1   0   0  0  0  0  0 | 3 0  3  0  0 0 0 | 1 3 0 0
.. o.3x.3o. .. ..      6  0 |  12   0   0 |   4   4   0   0   0   0 |  * 105   *   *   *   *   *   *  * |  1  2  0  0   1   0  0  0  0  0 | 2 1  1  2  0 0 0 | 1 2 1 0
.. .. x.3o.3o. ..      4  0 |   6   0   0 |   0   4   0   0   0   0 |  *   * 105   *   *   *   *   *  * |  0  2  1  0   1   0  0  0  0  0 | 1 2  0  2  1 0 0 | 1 1 2 0
.. oo3xo .. .. ..&#x   3  1 |   3   3   0 |   1   0   3   0   0   0 |  *   *   * 140   *   *   *   *  * |  0  0  0  1   3   0  0  0  0  0 | 0 0  3  3  0 0 0 | 0 3 1 0
.. .. xo3ox .. ..&#x   3  3 |   3   6   3 |   0   1   3   3   1   0 |  *   *   *   * 210   *   *   *  * |  0  0  0  0   2   2  0  0  0  0 | 0 0  1  4  1 0 0 | 0 2 2 0
.. .. .. ox3oo ..&#x   1  3 |   0   3   3 |   0   0   0   3   0   1 |  *   *   *   *   * 140   *   *  * |  0  0  0  0   0   3  1  0  0  0 | 0 0  0  3  3 0 0 | 0 1 3 0
.. .o3.o3.x .. ..      0  4 |   0   0   6 |   0   0   0   0   4   0 |  *   *   *   *   *   * 105   *  * |  0  0  0  0   1   0  0  1  2  0 | 0 0  1  2  0 2 1 | 0 2 1 1
.. .. .o3.x3.o ..      0  6 |   0   0  12 |   0   0   0   0   4   4 |  *   *   *   *   *   *   * 105  * |  0  0  0  0   0   1  0  0  2  1 | 0 0  0  2  1 1 2 | 0 1 2 1
.. .. .. .x3.o3.o      0  4 |   0   0   6 |   0   0   0   0   0   4 |  *   *   *   *   *   *   *   * 35 |  0  0  0  0   0   0  1  0  0  3 | 0 0  0  0  3 0 3 | 0 0 3 1
---------------------+-------+-------------+-------------------------+-----------------------------------+---------------------------------+------------------+--------
o.3o.3x.3o. .. ..     10  0 |  30   0   0 |  20  10   0   0   0   0 |  5   5   0   0   0   0   0   0  0 | 21  *  *  *   *   *  *  *  *  * | 2 0  1  0  0 0 0 | 1 2 0 0
.. o.3x.3o.3o. ..     10  0 |  30   0   0 |  10  20   0   0   0   0 |  0   5   5   0   0   0   0   0  0 |  * 42  *  *   *   *  *  *  *  * | 1 1  0  1  0 0 0 | 1 1 1 0
.. .. x.3o.3o.3o.      5  0 |  10   0   0 |   0  10   0   0   0   0 |  0   0   5   0   0   0   0   0  0 |  *  * 21  *   *   *  *  *  *  * | 0 2  0  0  1 0 0 | 1 0 2 0
oo3oo3xo .. .. ..&#x   4  1 |   6   4   0 |   4   0   6   0   0   0 |  1   0   0   4   0   0   0   0  0 |  *  *  * 35   *   *  *  *  *  * | 0 0  3  0  0 0 0 | 0 3 0 0
.. oo3xo3ox .. ..&#x   6  4 |  12  12   6 |   4   4  12   6   4   0 |  0   1   0   4   4   0   1   0  0 |  *  *  *  * 105   *  *  *  *  * | 0 0  1  2  0 0 0 | 0 2 1 0
.. .. xo3ox3oo ..&#x   4  6 |   6  12  12 |   0   4   6  12   4   4 |  0   0   1   0   4   4   0   1  0 |  *  *  *  *   * 105  *  *  *  * | 0 0  0  2  1 0 0 | 0 1 2 0
.. .. .. ox3oo3oo&#x   1  4 |   0   4   6 |   0   0   0   6   0   4 |  0   0   0   0   0   4   0   0  1 |  *  *  *  *   *   * 35  *  *  * | 0 0  0  0  3 0 0 | 0 0 3 0
.o3.o3.o3.x .. ..      0  5 |   0   0  10 |   0   0   0   0  10   0 |  0   0   0   0   0   0   5   0  0 |  *  *  *  *   *   *  * 21  *  * | 0 0  1  0  0 2 0 | 0 2 0 1
.. .o3.o3.x3.o ..      0 10 |   0   0  30 |   0   0   0   0  20  10 |  0   0   0   0   0   0   5   5  0 |  *  *  *  *   *   *  *  * 42  * | 0 0  0  1  0 1 1 | 0 1 1 1
.. .. .o3.x3.o3.o      0 10 |   0   0  30 |   0   0   0   0  10  20 |  0   0   0   0   0   0   0   5  5 |  *  *  *  *   *   *  *  *  * 21 | 0 0  0  0  1 0 2 | 0 0 2 1
---------------------+-------+-------------+-------------------------+-----------------------------------+---------------------------------+------------------+--------
o.3o.3x.3o.3o. ..     20  0 |  90   0   0 |  60  60   0   0   0   0 | 15  30  15   0   0   0   0   0  0 |  6  6  0  0   0   0  0  0  0  0 | 7 *  *  *  * * * | 1 1 0 0
.. o.3x.3o.3o.3o.     15  0 |  60   0   0 |  20  60   0   0   0   0 |  0  15  30   0   0   0   0   0  0 |  0  6  6  0   0   0  0  0  0  0 | * 7  *  *  * * * | 1 0 1 0
oo3oo3xo3ox .. ..&#x  10  5 |  30  20  10 |  20  10  30  10  10   0 |  5   5   0  20  10   0   5   0  0 |  1  0  0  5   5   0  0  1  0  0 | * * 21  *  * * * | 0 2 0 0
.. oo3xo3ox3oo ..&#x  10 10 |  30  30  30 |  10  20  30  30  20  10 |  0   5   5  10  20  10   5   5  0 |  0  1  0  0   5   5  0  0  1  0 | * *  * 42  * * * | 0 1 1 0
.. .. xo3ox3oo3oo&#x   5 10 |  10  20  30 |   0  10  10  30  10  20 |  0   0   5   0  10  20   0   5  5 |  0  0  1  0   0   5  5  0  0  1 | * *  *  * 21 * * | 0 0 2 0
.o3.o3.o3.x3.o ..      0 15 |   0   0  60 |   0   0   0   0  60  20 |  0   0   0   0   0   0  30  15  0 |  0  0  0  0   0   0  0  6  6  0 | * *  *  *  * 7 * | 0 1 0 1
.. .o3.o3.x3.o3.o      0 20 |   0   0  90 |   0   0   0   0  60  60 |  0   0   0   0   0   0  15  30 15 |  0  0  0  0   0   0  0  0  6  6 | * *  *  *  * * 7 | 0 0 1 1
---------------------+-------+-------------+-------------------------+-----------------------------------+---------------------------------+------------------+--------
o.3o.3x.3o.3o.3o.     35  0 | 210   0   0 | 140 210   0   0   0   0 | 35 105 105   0   0   0   0   0  0 | 21 42 21  0   0   0  0  0  0  0 | 7 7  0  0  0 0 0 | 1 * * *
oo3oo3xo3ox3oo ..&#x  20 15 |  90  60  60 |  60  60  90  60  60  20 | 15  30  15  60  60  20  30  15  0 |  6  6  0 15  30  15  0  6  6  0 | 1 0  6  6  0 1 0 | * 7 * *
.. oo3xo3ox3oo3oo&#x  15 20 |  60  60  90 |  20  60  60  90  60  60 |  0  15  30  20  60  60  15  30 15 |  0  6  6  0  15  30 15  0  6  6 | 0 1  0  6  6 0 1 | * * 7 *
.o3.o3.o3.x3.o3.o      0 35 |   0   0 210 |   0   0   0   0 210 140 |  0   0   0   0   0   0 105 105 35 |  0  0  0  0   0   0  0 21 42 21 | 0 0  0  0  0 7 7 | * * * 1

© 2004-2019
top of page