Acronym spo
Name small prismated octaexon,
runcinated octaexon
Circumradius sqrt(31)/4 = 1.391941
External
links
wikipedia  

Incidence matrix according to Dynkin symbol

x3o3o3x3o3o3o

. . . . . . . | 280 |   3   12 |   3   24   12   18 |  1  12  12   36   4  18  12 |  4  18  18  24   6  12   3 |  6  12  12   6  4  3 | 4  3  3 1
--------------+-----+----------+--------------------+-----------------------------+----------------------------+----------------------+----------
x . . . . . . |   2 | 420    * |   2    8    0    0 |  1   8   4   12   0   0   0 |  4  12   6   8   0   0   0 |  6   8   4   2  0  0 | 4  2  1 0
. . . x . . . |   2 |   * 1680 |   0    2    2    3 |  0   1   2    6   1   6   3 |  1   3   6   6   3   6   1 |  3   3   6   2  3  2 | 3  1  2 1
--------------+-----+----------+--------------------+-----------------------------+----------------------------+----------------------+----------
x3o . . . . . |   3 |   3    0 | 280    *    *    * |  1   4   0    0   0   0   0 |  4   6   0   0   0   0   0 |  6   4   0   0  0  0 | 4  1  0 0
x . . x . . . |   4 |   2    2 |   * 1680    *    * |  0   1   1    3   0   0   0 |  1   3   3   3   0   0   0 |  3   3   3   1  0  0 | 3  1  1 0
. . o3x . . . |   3 |   0    3 |   *    * 1120    * |  0   0   1    0   1   3   0 |  1   0   3   0   3   3   0 |  3   0   3   0  3  1 | 3  0  1 1
. . . x3o . . |   3 |   0    3 |   *    *    * 1680 |  0   0   0    2   0   2   2 |  0   1   2   4   1   4   1 |  1   2   4   2  2  2 | 2  1  2 1
--------------+-----+----------+--------------------+-----------------------------+----------------------------+----------------------+----------
x3o3o . . . .    4 |   6    0 |   4    0    0    0 | 70   *   *    *   *   *   *   4   0   0   0   0   0   0 |  6   0   0   0  0  0 | 4  0  0 0
x3o . x . . .    6 |   6    3 |   2    3    0    0 |  * 560   *    *   *   *   * |  1   3   0   0   0   0   0 |  3   3   0   0  0  0 | 3  1  0 0
x . o3x . . .    6 |   3    6 |   0    3    2    0 |  *   * 560    *   *   *   * |  1   0   3   0   0   0   0 |  3   0   3   0  0  0 | 3  0  1 0
x . . x3o . .    6 |   3    6 |   0    3    0    2 |  *   *   * 1680   *   *   * |  0   1   1   2   0   0   0 |  1   2   2   1  0  0 | 2  1  1 0
. o3o3x . . .    4 |   0    6 |   0    0    4    0 |  *   *   *    * 280   *   * |  1   0   0   0   3   0   0 |  3   0   0   0  3  0 | 3  0  0 1
. . o3x3o . .    6 |   0   12 |   0    0    4    4 |  *   *   *    *   * 840   * |  0   0   1   0   1   2   0 |  1   0   2   0  2  1 | 2  0  1 1
. . . x3o3o .    4 |   0    6 |   0    0    0    4 |  *   *   *    *   *   * 840 |  0   0   0   2   0   2   1 |  0   1   2   2  1  2 | 1  1  2 1
--------------+-----+----------+--------------------+-----------------------------+----------------------------+----------------------+----------
x3o3o3x . . .   20 |  30   30 |  20   30   20    0 |  5  10  10    0   5   0   0 | 56   *   *   *   *   *   * |  3   0   0   0  0  0 | 3  0  0 0
x3o . x3o . .    9 |   9    9 |   3    9    0    3 |  0   3   0    3   0   0   0 |  * 560   *   *   *   *   * |  1   2   0   0  0  0 | 2  1  0 0
x . o3x3o . .   12 |   6   24 |   0   12    8    8 |  0   0   4    4   0   2   0 |  *   * 420   *   *   *   * |  1   0   2   0  0  0 | 2  0  1 0
x . . x3o3o .    8 |   4   12 |   0    6    0    8 |  0   0   0    4   0   0   2 |  *   *   * 840   *   *   * |  0   1   1   1  0  0 | 1  1  1 0
. o3o3x3o . .   10 |   0   30 |   0    0   20   10 |  0   0   0    0   5   5   0 |  *   *   *   * 168   *   * |  1   0   0   0  2  0 | 2  0  0 1
. . o3x3o3o .   10 |   0   30 |   0    0   10   20 |  0   0   0    0   0   5   5 |  *   *   *   *   * 336   * |  0   0   1   0  1  1 | 1  0  1 1
. . . x3o3o3o    5 |   0   10 |   0    0    0   10 |  0   0   0    0   0   0   5 |  *   *   *   *   *   * 168 |  0   0   0   2  0  2 | 0  1  2 1
--------------+-----+----------+--------------------+-----------------------------+----------------------------+----------------------+----------
x3o3o3x3o . .   60 |  90  180 |  60  180  120   60 | 15  60  60   60  30  30   0 |  6  20  15   0   6   0   0 | 28   *   *   *  *  * | 2  0  0 0
x3o . x3o3o .   12 |  12   18 |   4   18    0   12 |  0   6   0   12   0   0   3 |  0   4   0   3   0   0   0 |  * 280   *   *  *  * | 1  1  0 0
x . o3x3o3o .   20 |  10   60 |   0   30   20   40 |  0   0  10   20   0  10  10 |  0   0   5   5   0   2   0 |  *   * 168   *  *  * | 1  0  1 0
x . . x3o3o3o   10 |   5   20 |   0   10    0   20 |  0   0   0   10   0   0  10 |  0   0   0   5   0   0   2 |  *   *   * 168  *  * | 0  1  1 0
. o3o3x3o3o .   20 |   0   90 |   0    0   60   60 |  0   0   0    0  15  30  15 |  0   0   0   0   6   6   0 |  *   *   *   * 56  * | 1  0  0 1
. . o3x3o3o3o   15 |   0   60 |   0    0   20   60 |  0   0   0    0   0  15  30 |  0   0   0   0   0   6   6 |  *   *   *   *  * 56 | 0  0  1 1
--------------+-----+----------+--------------------+-----------------------------+----------------------------+----------------------+----------
x3o3o3x3o3o .  140 | 210  630 | 140  630  420  420 | 35 210 210  420 105 210 105 | 21 140 105 105  42  42   0 |  7  35  21   0  7  0 | 8  *  * *
x3o . x3o3o3o   15 |  15   30 |   5   30    0   30 |  0  10   0   30   0   0  15 |  0  10   0  15   0   0   3 |  0   5   0   3  0  0 | * 56  * *
x . o3x3o3o3o   30 |  15  120 |   0   60   40  120 |  0   0  20   60   0  30  60 |  0   0  15  30   0  12  12 |  0   0   6   6  0  2 | *  * 28 *
. o3o3x3o3o3o   35 |   0  210 |   0    0  140  210 |  0   0   0    0  35 105 105 |  0   0   0   0  21  42  21 |  0   0   0   0  7  7 | *  *  * 8

ooo3ooo3oox3xxo3ooo3oxx&#xt   → both heights = sqrt(4/7) = 0.755929
(bril || pseudo sril || spil)

...

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