Acronym pexhax
Name partially expanded hemihexeract
Circumradius sqrt(7)/2 = 1.322876
Coordinates (1/sqrt(8), 1/sqrt(8), 3/sqrt(8); 1/sqrt(8), 1/sqrt(8), 1/sqrt(8))   & all permutations of either coord. subset, all even changes of sign in either coord. subset
Confer
general polytopal classes:
scaliform   partial Stott expansions  
External
links
polytopewiki  

Incidence matrix according to Dynkin symbol

xo3xx3ox xo3oo3ox&#zx   → height = 0
(tegum sum of 2 bi-inverted tettuts)

o.3o.3o. o.3o.3o.     & | 96 |  1  2   3   6 |  2  1   6  3   9   6  18 | 1  3  6  1  9  3  12  18   8   6 |  3  2  3 12  3  5  8  6  2 | 1 3  5 1  2
------------------------+----+---------------+--------------------------+----------------------------------+----------------------------+------------
x. .. .. .. .. ..     & |  2 | 48  *   *   * |  2  0   0  0   6   0   0 | 1  0  0  0  6  3   6   0   0   0 |  0  0  3  6  3  2  0  0  0 | 0 3  2 1  0
.. x. .. .. .. ..     & |  2 |  * 96   *   * |  1  1   3  0   0   3   0 | 1  3  3  0  6  0   0   9   0   0 |  3  1  3  9  0  0  4  3  0 | 1 3  4 0  1
.. .. .. x. .. ..     & |  2 |  *  * 144   * |  0  0   2  2   0   0   4 | 0  1  4  1  0  0   2   4   4   2 |  2  2  0  2  1  2  4  2  2 | 1 1  2 1  2
oo3oo3oo oo3oo3oo&#x    |  2 |  *  *   * 288 |  0  0   0  0   2   1   4 | 0  0  0  0  2  1   4   4   2   2 |  0  0  1  4  2  2  2  2  1 | 0 2  2 1  1
------------------------+----+---------------+--------------------------+----------------------------------+----------------------------+------------
x.3x. .. .. .. ..     & |  6 |  3  3   0   0 | 32  *   *  *   *   *   * | 1  0  0  0  3  0   0   0   0   0 |  0  0  3  3  0  0  0  0  0 | 0 3  1 0  0
.. x.3o. .. .. ..     & |  3 |  0  3   0   0 |  * 32   *  *   *   *   * | 1  3  0  0  3  0   0   0   0   0 |  3  0  3  6  0  0  0  0  0 | 1 3  3 0  0
.. x. .. x. .. ..     & |  4 |  0  2   2   0 |  *  * 144  *   *   *   * | 0  1  2  0  0  0   0   2   0   0 |  2  1  0  2  0  0  2  1  0 | 1 1  2 0  1
.. .. .. x.3o. ..     & |  3 |  0  0   3   0 |  *  *   * 96   *   *   * | 0  0  2  1  0  0   0   0   2   0 |  1  2  0  0  0  1  2  0  2 | 1 0  1 1  2
xo .. .. .. .. ..&#x  & |  3 |  1  0   0   2 |  *  *   *  * 288   *   * | 0  0  0  0  1  1   2   0   0   0 |  0  0  1  2  2  1  0  0  0 | 0 2  1 1  0
.. xx .. .. .. ..&#x    |  4 |  0  2   0   2 |  *  *   *  *   * 144   * | 0  0  0  0  2  0   0   4   0   0 |  0  0  1  4  0  0  2  2  0 | 0 2  2 0  1
.. .. .. xo .. ..&#x  & |  3 |  0  0   1   2 |  *  *   *  *   *   * 576 | 0  0  0  0  0  0   1   1   1   1 |  0  0  0  1  1  1  1  1  1 | 0 1  1 1  1
------------------------+----+---------------+--------------------------+----------------------------------+----------------------------+------------
x.3x.3o. .. .. ..     &  12 |  6 12   0   0 |  4  4   0  0   0   0   0 | 8  *  *  *  *  *   *   *   *   * |  0  0  3  0  0  0  0  0  0 | 0 3  0 0  0
.. x.3o. x. .. ..     &   6 |  0  6   3   0 |  0  2   3  0   0   0   0 | * 48  *  *  *  *   *   *   *   * |  2  0  0  2  0  0  0  0  0 | 1 1  2 0  0
.. x. .. x.3o. ..     &   6 |  0  3   6   0 |  0  0   3  2   0   0   0 | *  * 96  *  *  *   *   *   *   * |  1  1  0  0  0  0  1  0  0 | 1 0  1 0  1
.. .. .. x.3o.3o.     &   4 |  0  0   6   0 |  0  0   0  4   0   0   0 | *  *  * 24  *  *   *   *   *   * |  0  2  0  0  0  0  0  0  2 | 1 0  0 1  2
xo3xx .. .. .. ..&#x  &   9 |  3  6   0   6 |  1  1   0  0   3   3   0 | *  *  *  * 96  *   *   *   *   * |  0  0  1  2  0  0  0  0  0 | 0 2  1 0  0
xo .. ox .. .. ..&#x      4 |  2  0   0   4 |  0  0   0  0   4   0   0 | *  *  *  *  * 72   *   *   *   * |  0  0  1  0  2  0  0  0  0 | 0 2  0 1  0
xo .. .. .. .. ox&#x  &   4 |  1  0   1   4 |  0  0   0  0   2   0   2 | *  *  *  *  *  * 288   *   *   * |  0  0  0  1  1  1  0  0  0 | 0 1  1 1  0
.. xx .. xo .. ..&#x  &   6 |  0  3   2   4 |  0  0   1  0   0   2   2 | *  *  *  *  *  *   * 288   *   * |  0  0  0  1  0  0  1  1  0 | 0 1  1 0  1
.. .. .. xo3oo ..&#x  &   4 |  0  0   3   3 |  0  0   0  1   0   0   3 | *  *  *  *  *  *   *   * 192   * |  0  0  0  0  0  1  1  0  1 | 0 0  1 1  1
.. .. .. xo .. ox&#x      4 |  0  0   2   4 |  0  0   0  0   0   0   4 | *  *  *  *  *  *   *   *   * 144 |  0  0  0  0  1  0  0  1  1 | 0 1  0 1  1
------------------------+----+---------------+--------------------------+----------------------------------+----------------------------+------------
.. x.3o. x.3o. ..     &   9 |  0  9   9   0 |  0  3   9  3   0   0   0 | 0  3  3  0  0  0   0   0   0   0 | 32  *  *  *  *  *  *  *  * | 1 0  1 0  0
.. x. .. x.3o.3o.     &   8 |  0  4  12   0 |  0  0   6  8   0   0   0 | 0  0  4  2  0  0   0   0   0   0 |  * 24  *  *  *  *  *  *  * | 1 0  0 0  1
xo3xx3ox .. .. ..&#x     24 | 12 24   0  24 |  8  8   0  0  24  12   0 | 2  0  0  0  8  6   0   0   0   0 |  *  * 12  *  *  *  *  *  * | 0 2  0 0  0
xo3xx .. .. .. ox&#x  &  12 |  3  9   3  12 |  1  2   3  0   6   6   6 | 0  1  0  0  2  0   3   3   0   0 |  *  *  * 96  *  *  *  *  * | 0 1  1 0  0
xo .. ox xo .. ox&#zx     8 |  4  0   4  16 |  0  0   0  0  16   0  16 | 0  0  0  0  0  4   8   0   0   4 |  *  *  *  * 36  *  *  *  * | 0 1  0 1  0
xo .. .. .. oo3ox&#x  &   5 |  1  0   3   6 |  0  0   0  1   3   0   6 | 0  0  0  0  0  0   3   0   2   0 |  *  *  *  *  * 96  *  *  * | 0 0  1 1  0
.. xx .. xo3oo ..&#x  &   8 |  0  4   6   6 |  0  0   3  2   0   3   6 | 0  0  1  0  0  0   0   3   2   0 |  *  *  *  *  *  * 96  *  * | 0 0  1 0  1
.. xx .. xo .. ox&#x      8 |  0  4   4   8 |  0  0   2  0   0   4   8 | 0  0  0  0  0  0   0   4   0   2 |  *  *  *  *  *  *  * 72  * | 0 1  0 0  1
.. .. .. xo3oo3ox&#x      8 |  0  0  12  12 |  0  0   0  8   0   0  24 | 0  0  0  2  0  0   0   0   8   6 |  *  *  *  *  *  *  *  * 24 | 0 0  0 1  1
------------------------+----+---------------+--------------------------+----------------------------------+----------------------------+------------
.. x.3o. x.3o.3o.     &  12 |  0 12  18   0 |  0  4  18 12   0   0   0 | 0  6 12  3  0  0   0   0   0   0 |  4  3  0  0  0  0  0  0  0 | 8 *  * *  *
xo3xx3ox xo .. ox&#zx    48 | 24 48  24  96 | 16 16  24  0  96  48  96 | 4  8  0  0 32 24  48  48   0  24 |  0  0  4 16  6  0  0 12  0 | * 6  * *  *
xo3xx .. .. oo3ox&#x  &  15 |  3 12   9  18 |  1  3   9  3   9   9  18 | 0  3  3  0  3  0   9   9   6   0 |  1  0  0  3  0  3  3  0  0 | * * 32 *  *
xo .. ox xo3oo3ox&#zx    16 |  8  0  24  48 |  0  0   0 16  48   0  96 | 0  0  0  4  0 12  48   0  32  24 |  0  0  0  0  6 16  0  0  4 | * *  * 6  *
.. xx .. xo3oo3ox&#x     16 |  0  8  24  24 |  0  0  12 16   0  12  48 | 0  0  8  4  0  0   0  24  16  12 |  0  2  0  0  0  0  8  6  2 | * *  * * 12

© 2004-2021
top of page