Acronym stoxog
Name small terated hexeractihexacontatetrapeton,
pentellated hexeract,
pentellated hexacross
Circumradius sqrt[2+1/sqrt(2)] = 1.645329
Inradius
wrt. hix
[1+3 sqrt(2)]/sqrt(12) = 1.513420
Inradius
wrt. penp
[5+sqrt(2)]/sqrt(20) = 1.434262
Inradius
wrt. squatet
[1+2 sqrt(2)]/sqrt(8) = 1.353553
Inradius
wrt. tracube
[3+sqrt(2)]/sqrt(12) = 1.274274
Inradius
wrt. pent
(1+sqrt(2))/2 = 1.207107
Coordinates ((1+sqrt(2))/2, 1/2, 1/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign
Volume [833+579 sqrt(2)]/45 = 36.707326
Surface [1080+300 sqrt(2)+601 sqrt(3)+30 sqrt(5)]/15 = 174.153910
Dihedral angles
(at margins)
Confer
analogs:
maximal expanded hypercube eCn  
External
links
wikipedia   polytopewiki  

As abstract polytope stoxog is isomorphic to quitoxog.


Incidence matrix according to Dynkin symbol

x3o3o3o3o4x

. . . . . . | 384 |   5   5 |   10   20  10 |  10   30   30  10 |   5  20  30  20   5 |  1   5  10  10  5  1
------------+-----+---------+---------------+-------------------+---------------------+---------------------
x . . . . . |   2 | 960   * |    4    4   0 |   6   12    6   0 |   4  12  12   4   0 |  1   4   6   4  1  0
. . . . . x |   2 |   * 960 |    0    4   4 |   0    6   12   6 |   0   4  12  12   4 |  0   1   4   6  4  1
------------+-----+---------+---------------+-------------------+---------------------+---------------------
x3o . . . . |   3 |   3   0 | 1280    *   * |   3    3    0   0 |   3   6   3   0   0 |  1   3   3   1  0  0
x . . . . x |   4 |   2   2 |    * 1920   * |   0    3    3   0 |   0   3   6   3   0 |  0   1   3   3  1  0
. . . . o4x |   4 |   0   4 |    *    * 960 |   0    0    3   3 |   0   0   3   6   3 |  0   0   1   3  3  1
------------+-----+---------+---------------+-------------------+---------------------+---------------------
x3o3o . . .    4 |   6   0 |    4    0   0 | 960    *    *   * |   2   2   0   0   0 |  1   2   1   0  0  0
x3o . . . x    6 |   6   3 |    2    3   0 |   * 1920    *   * |   0   2   2   0   0 |  0   1   2   1  0  0
x . . . o4x    8 |   4   8 |    0    4   2 |   *    * 1440   * |   0   0   2   2   0 |  0   0   1   2  1  0
. . . o3o4x    8 |   0  12 |    0    0   6 |   *    *    * 480 |   0   0   0   2   2 |  0   0   0   1  2  1
------------+-----+---------+---------------+-------------------+---------------------+---------------------
x3o3o3o . .    5 |  10   0 |   10    0   0 |   5    0    0   0 | 384   *   *   *   * |  1   1   0   0  0  0
x3o3o . . x    8 |  12   4 |    8    6   0 |   2    4    0   0 |   * 960   *   *   * |  0   1   1   0  0  0
x3o . . o4x   12 |  12  12 |    4   12   3 |   0    4    3   0 |   *   * 960   *   * |  0   0   1   1  0  0
x . . o3o4x   16 |   8  24 |    0   12  12 |   0    0    6   2 |   *   *   * 480   * |  0   0   0   1  1  0
. . o3o3o4x   16 |   0  32 |    0    0  24 |   0    0    0   8 |   *   *   *   * 120 |  0   0   0   0  1  1
------------+-----+---------+---------------+-------------------+---------------------+---------------------
x3o3o3o3o .    6 |  15   0 |   20    0   0 |  15    0    0   0 |   6   0   0   0   0 | 64   *   *   *  *  *
x3o3o3o . x   10 |  20   5 |   20   10   0 |  10   10    0   0 |   2   5   0   0   0 |  * 192   *   *  *  *
x3o3o . o4x   16 |  24  16 |   16   24   4 |   4   16    6   0 |   0   4   4   0   0 |  *   * 240   *  *  *
x3o . o3o4x   24 |  24  36 |    8   36  18 |   0   12   18   3 |   0   0   6   3   0 |  *   *   * 160  *  *
x . o3o3o4x   32 |  16  64 |    0   32  48 |   0    0   24  16 |   0   0   0   8   2 |  *   *   *   * 60  *
. o3o3o3o4x   32 |   0  80 |    0    0  80 |   0    0    0  40 |   0   0   0   0  10 |  *   *   *   *  * 12

ox3oo4xx xo3oo4xx&#zx   → height = 0
(tegum sum of 2 interchanged cubesircoes)

o.3o.4o. o.3o.4o.     & | 384 |   3   2   2   3 |   3   6   6   1   2  1    9   12 |  1   6   6   3   6   3   4   9   6   18   6  12 |  2  2  3   6  3   5   8  12  18   9  12 |  1  2  1  1   5  4   6   9  3
------------------------+-----+-----------------+----------------------------------+-------------------------------------------------+-----------------------------------------+------------------------------
.. .. x. .. .. ..     & |   2 | 576   *   *   * |   2   2   2   0   0  0    0    2 |  1   4   4   1   2   1   0   1   0    4   2   4 |  2  2  2   4  2   0   2   2   6   4   6 |  1  2  1  0   1  2   2   5  2
.. .. .. x. .. ..     & |   2 |   * 384   *   * |   0   3   0   1   1  0    3    0 |  0   3   0   3   3   0   3   3   3    6   0   0 |  1  0  3   3  0   4   6   6   6   3   0 |  1  1  0  1   4  3   3   3  0
.. .. .. .. .. x.     & |   2 |   *   * 384   * |   0   0   3   0   1  1    0    3 |  0   0   3   0   3   3   0   3   0    3   3   6 |  0  1  0   3  3   0   1   3   9   3   9 |  0  1  1  0   1  1   3   6  3
oo3oo4oo oo3oo4oo&#x    |   2 |   *   *   * 576 |   0   0   0   0   0  0    4    4 |  0   0   0   0   0   0   2   4   4    8   2   4 |  0  0  0   0  0   4   4   8   8   4   4 |  0  0  0  1   4  2   4   4  1
------------------------+-----+-----------------+----------------------------------+-------------------------------------------------+-----------------------------------------+------------------------------
.. o.4x. .. .. ..     & |   4 |   4   0   0   0 | 288   *   *   *   *  *    *    * |  1   2   2   0   0   0   0   0   0    0   1   0 |  2  2  1   2  1   0   0   0   0   2   2 |  1  2  1  0   0  1   0   2  1
.. .. x. x. .. ..     & |   4 |   2   2   0   0 |   * 576   *   *   *  *    *    * |  0   2   0   1   1   0   0   0   0    2   0   0 |  1  0  2   2  0   0   2   1   2   2   0 |  1  1  0  0   1  2   1   2  0
.. .. x. .. .. x.     & |   4 |   2   0   2   0 |   *   * 576   *   *  *    *    * |  0   0   2   0   1   1   0   0   0    0   0   2 |  0  1  0   2  2   0   0   0   3   0   4 |  0  1  1  0   0  0   1   3  2
.. .. .. x.3o. ..     & |   3 |   0   3   0   0 |   *   *   * 128   *  *    *    * |  0   0   0   3   0   0   3   0   0    0   0   0 |  0  0  3   0  0   3   6   0   0   0   0 |  1  0  0  1   3  3   0   0  0
.. .. .. x. .. x.     & |   4 |   0   2   2   0 |   *   *   *   * 192  *    *    * |  0   0   0   0   3   0   0   3   0    0   0   0 |  0  0  0   3  0   0   0   3   6   0   0 |  0  1  0  0   1  0   3   3  0
.. .. .. .. o.4x.     & |   4 |   0   0   4   0 |   *   *   *   *   * 96    *    * |  0   0   0   0   0   3   0   0   0    0   3   0 |  0  0  0   0  3   0   0   0   0   3   6 |  0  0  1  0   0  1   0   3  3
ox .. .. .. .. ..&#x  & |   3 |   0   1   0   2 |   *   *   *   *   *  * 1152    * |  0   0   0   0   0   0   1   1   2    2   0   0 |  0  0  0   0  0   3   2   4   2   1   0 |  0  0  0  1   3  1   2   1  0
.. .. xx .. .. ..&#x  & |   4 |   1   0   1   2 |   *   *   *   *   *  *    * 1152 |  0   0   0   0   0   0   0   1   0    2   1   2 |  0  0  0   0  0   0   1   2   4   2   3 |  0  0  0  0   1  1   2   3  1
------------------------+-----+-----------------+----------------------------------+-------------------------------------------------+-----------------------------------------+------------------------------
o.3o.4x. .. .. ..     &    8 |  12   0   0   0 |   6   0   0   0   0  0    0    0 | 48   *   *   *   *   *   *   *   *    *   *   * |  2  2  0   0  0   0   0   0   0   0   0 |  1  2  1  0   0  0   0   0  0
.. o.4x. x. .. ..     &    8 |   8   4   0   0 |   2   4   0   0   0  0    0    0 |  * 288   *   *   *   *   *   *   *    *   *   * |  1  0  1   1  0   0   0   0   0   1   0 |  1  1  0  0   0  1   0   1  0
.. o.4x. .. .. x.     &    8 |   8   0   4   0 |   2   0   4   0   0  0    0    0 |  *   * 288   *   *   *   *   *   *    *   *   * |  0  1  0   1  1   0   0   0   0   0   1 |  0  1  1  0   0  0   0   1  1
.. .. x. x.3o. ..     &    6 |   3   6   0   0 |   0   3   0   2   0  0    0    0 |  *   *   * 192   *   *   *   *   *    *   *   * |  0  0  2   0  0   0   2   0   0   0   0 |  1  0  0  0   1  2   0   0  0
.. .. x. x. .. x.     &    8 |   4   4   4   0 |   0   2   2   0   2  0    0    0 |  *   *   *   * 288   *   *   *   *    *   *   * |  0  0  0   2  0   0   0   0   2   0   0 |  0  1  0  0   0  0   1   2  0
.. .. x. .. o.4x.     &    8 |   4   0   8   0 |   0   0   4   0   0  2    0    0 |  *   *   *   *   * 144   *   *   *    *   *   * |  0  0  0   0  2   0   0   0   0   0   2 |  0  0  1  0   0  0   0   1  2
ox3oo .. .. .. ..&#x  &    4 |   0   3   0   3 |   0   0   0   1   0  0    3    0 |  *   *   *   *   *   * 384   *   *    *   *   * |  0  0  0   0  0   2   2   0   0   0   0 |  0  0  0  1   2  1   0   0  0
ox .. xx .. .. ..&#x  &    6 |   1   2   2   4 |   0   0   0   0   1  0    2    2 |  *   *   *   *   *   *   * 576   *    *   *   * |  0  0  0   0  0   0   0   2   2   0   0 |  0  0  0  0   1  0   2   1  0
ox .. .. xo .. ..&#x       4 |   0   2   0   4 |   0   0   0   0   0  0    4    0 |  *   *   *   *   *   *   *   * 576    *   *   * |  0  0  0   0  0   2   0   2   0   0   0 |  0  0  0  1   2  0   1   0  0
ox .. .. .. .. xx&#x  &    6 |   2   2   1   4 |   0   1   0   0   0  0    2    2 |  *   *   *   *   *   *   *   *   * 1152   *   * |  0  0  0   0  0   0   1   1   1   1   0 |  0  0  0  0   1  1   1   1  0
.. oo4xx .. .. ..&#x  &    8 |   4   0   4   4 |   1   0   0   0   0  1    0    4 |  *   *   *   *   *   *   *   *   *    * 288   * |  0  0  0   0  0   0   0   0   0   2   2 |  0  0  0  0   0  1   0   2  1
.. .. xx .. .. xx&#x       8 |   4   0   4   4 |   0   0   2   0   0  0    0    4 |  *   *   *   *   *   *   *   *   *    *   * 576 |  0  0  0   0  0   0   0   0   2   0   2 |  0  0  0  0   0  0   1   2  1
------------------------+-----+-----------------+----------------------------------+-------------------------------------------------+-----------------------------------------+------------------------------
o.3o.4x. x. .. ..     &   16 |  24   8   0   0 |  12  12   0   0   0  0    0    0 |  2   6   0   0   0   0   0   0   0    0   0   0 | 48  *  *   *  *   *   *   *   *   *   * |  1  1  0  0   0  0   0   0  0
o.3o.4x. .. .. x.     &   16 |  24   0   8   0 |  12   0  12   0   0  0    0    0 |  2   0   6   0   0   0   0   0   0    0   0   0 |  * 48  *   *  *   *   *   *   *   *   * |  0  1  1  0   0  0   0   0  0
.. o.4x. x.3o. ..     &   12 |  12  12   0   0 |   3  12   0   4   0  0    0    0 |  0   3   0   4   0   0   0   0   0    0   0   0 |  *  * 96   *  *   *   *   *   *   *   * |  1  0  0  0   0  1   0   0  0
.. o.4x. x. .. x.     &   16 |  16   8   8   0 |   4   8   8   0   4  0    0    0 |  0   2   2   0   4   0   0   0   0    0   0   0 |  *  *  * 144  *   *   *   *   *   *   * |  0  1  0  0   0  0   0   1  0
.. o.4x. .. o.4x.     &   16 |  16   0  16   0 |   4   0  16   0   0  4    0    0 |  0   0   4   0   0   4   0   0   0    0   0   0 |  *  *  *   * 72   *   *   *   *   *   * |  0  0  1  0   0  0   0   0  1
ox3oo .. xo .. ..&#x  &    5 |   0   4   0   6 |   0   0   0   1   0  0    9    0 |  0   0   0   0   0   0   2   0   3    0   0   0 |  *  *  *   *  * 384   *   *   *   *   * |  0  0  0  1   1  0   0   0  0
ox3oo .. .. .. xx&#x  &    8 |   3   6   1   6 |   0   3   0   2   0  0    6    3 |  0   0   0   1   0   0   2   0   0    3   0   0 |  *  *  *   *  *   * 384   *   *   *   * |  0  0  0  0   1  1   0   0  0
ox .. xx xo .. ..&#x  &    8 |   2   4   2   8 |   0   1   0   0   1  0    8    4 |  0   0   0   0   0   0   0   2   2    2   0   0 |  *  *  *   *  *   *   * 576   *   *   * |  0  0  0  0   1  0   1   0  0
ox .. xx .. .. xx&#x  &   12 |   6   4   6   8 |   0   2   3   0   2  0    4    8 |  0   0   0   0   1   0   0   2   0    2   0   2 |  *  *  *   *  *   *   *   * 576   *   * |  0  0  0  0   0  0   1   1  0
.. oo4xx xo .. ..&#x  &   12 |   8   4   4   8 |   2   4   0   0   0  1    4    8 |  0   1   0   0   0   0   0   0   0    4   2   0 |  *  *  *   *  *   *   *   *   * 288   * |  0  0  0  0   0  1   0   1  0
.. oo4xx .. .. xx&#x  &   16 |  12   0  12   8 |   2   0   8   0   0  2    0   12 |  0   0   1   0   0   1   0   0   0    0   2   4 |  *  *  *   *  *   *   *   *   *   * 288 |  0  0  0  0   0  0   0   1  1
------------------------+-----+-----------------+----------------------------------+-------------------------------------------------+-----------------------------------------+------------------------------
o.3o.4x. x.3o. ..     &   24 |  36  24   0   0 |  18  36   0   8   0  0    0    0 |  3  18   0  12   0   0   0   0   0    0   0   0 |  3  0  6   0  0   0   0   0   0   0   0 | 16  *  *  *   *  *   *   *  *
o.3o.4x. x. .. x.     &   32 |  48  16  16   0 |  24  24  24   0   8  0    0    0 |  4  12  12   0  12   0   0   0   0    0   0   0 |  2  2  0   6  0   0   0   0   0   0   0 |  * 24  *  *   *  *   *   *  *
o.3o.4x. .. o.4x.     &   32 |  48   0  32   0 |  24   0  48   0   0  8    0    0 |  4   0  24   0   0  12   0   0   0    0   0   0 |  0  4  0   0  6   0   0   0   0   0   0 |  *  * 12  *   *  *   *   *  *
ox3oo .. xo3oo ..&#x       6 |   0   6   0   9 |   0   0   0   2   0  0   18    0 |  0   0   0   0   0   0   6   0   9    0   0   0 |  0  0  0   0  0   6   0   0   0   0   0 |  *  *  * 64   *  *   *   *  *
ox3oo .. xo .. xx&#x  &   10 |   3   8   2  12 |   0   3   0   2   1  0   18    6 |  0   0   0   1   0   0   4   3   6    6   0   0 |  0  0  0   0  0   2   2   3   0   0   0 |  *  *  *  * 192  *   *   *  *
ox3oo .. .. oo4xx&#x  &   16 |  12  12   4  12 |   3  12   0   4   0  1   12   12 |  0   3   0   4   0   0   4   0   0   12   3   0 |  0  0  1   0  0   0   4   0   0   3   0 |  *  *  *  *   * 96   *   *  *
ox .. xx xo .. xx&#x      16 |   8   8   8  16 |   0   4   4   0   4  0   16   16 |  0   0   0   0   2   0   0   8   4    8   0   4 |  0  0  0   0  0   0   0   4   4   0   0 |  *  *  *  *   *  * 144   *  *
ox .. xx .. oo4xx&#x  &   24 |  20   8  16  16 |   4   8  12   0   4  2    8   24 |  0   2   2   0   4   1   0   4   0    8   4   8 |  0  0  0   1  0   0   0   0   4   2   2 |  *  *  *  *   *  *   * 144  *
.. oo4xx .. oo4xx&#x      32 |  32   0  32  16 |   8   0  32   0   0  8    0   32 |  0   0   8   0   0   8   0   0   0    0   8  16 |  0  0  0   0  2   0   0   0   0   0   8 |  *  *  *  *   *  *   *   * 36

© 2004-2021
top of page