Acronym spila (old: spilal spil) Name small prismated heptapeton atop inverted small prismated heptapeton Circumradius sqrt(7)/2 = 1.322876 Confer general polytopal classes: segmentoexa   scaliform   fundamental lace prisms

Incidence matrix according to Dynkin symbol

```xo3oo3ox3xo3oo3ox&#x   → height = 1/sqrt(7) = 0.377964
(spil || inv spil)

o.3o.3o.3o.3o.3o.    & | 280 |   3    9    9 |   3   18   9   9   27   27 |  1   9   9  18   3   9   3  12   18   45   18  12  18 |  3   9   9   6  3  3   6  21  15  27   27  21  15 |  3  3  3  1  9   9  10  12   3  12   9  3 | 1  4  6  4
-----------------------+-----+---------------+----------------------------+-------------------------------------------------------+---------------------------------------------------+-------------------------------------------+-----------
x. .. .. .. .. ..    & |   2 | 420    *    * |   2    6   0   0    6    0 |  1   6   3   6   0   0   0   6    3   12    6   0   0 |  3   6   3   2  0  0   3  12   8   6    9   6   0 |  3  2  1  0  6   5   6   7   2   3   3  0 | 1  3  4  3
.. .. .. x. .. ..    & |   2 |   * 1260    * |   0    2   2   2    0    2 |  0   1   2   4   1   4   1   0    1    4    0   2   4 |  1   2   4   2  2  2   1   2   0   6    2   4   6 |  2  1  2  1  4   2   2   1   0   5   2  2 | 1  3  3  1
oo3oo3oo3oo3oo3oo&#x   |   2 |   *    * 1260 |   0    0   0   0    4    4 |  0   0   0   0   0   0   0   2    4    8    4   2   4 |  0   0   0   0  0  0   2   4   4   8    8   4   4 |  0  0  0  0  4   4   2   4   1   4   4  1 | 0  2  4  2
-----------------------+-----+---------------+----------------------------+-------------------------------------------------------+---------------------------------------------------+-------------------------------------------+-----------
x.3o. .. .. .. ..    & |   3 |   3    0    0 | 280    *   *   *    *    * |  1   3   0   0   0   0   0   3    0    0    0   0   0 |  3   3   0   0  0  0   3   6   3   0    0   0   0 |  3  1  0  0  6   3   3   3   1   0   0  0 | 1  3  3  2
x. .. .. x. .. ..    & |   4 |   2    2    0 |   * 1260   *   *    *    * |  0   1   1   2   0   0   0   0    0    2    0   0   0 |  1   2   2   1  0  0   0   2   0   2    1   2   0 |  2  1  1  0  2   1   2   1   0   2   1  0 | 1  2  2  1
.. .. o.3x. .. ..    & |   3 |   0    3    0 |   *    * 840   *    *    * |  0   0   1   0   1   2   0   0    0    0    0   0   2 |  1   0   2   0  2  1   0   0   0   2    0   0   4 |  2  0  1  1  2   0   0   0   0   3   1  2 | 1  3  2  0
.. .. .. x.3o. ..    & |   3 |   0    3    0 |   *    *   * 840    *    * |  0   0   0   2   0   2   1   0    0    0    0   1   0 |  0   1   2   2  1  2   1   0   0   1    0   2   2 |  1  1  2  1  3   2   1   0   0   2   0  1 | 1  2  2  1
xo .. .. .. .. ..&#x & |   3 |   1    0    2 |   *    *   *   * 2520    * |  0   0   0   0   0   0   0   1    1    2    2   0   0 |  0   0   0   0  0  0   1   2   3   2    4   1   0 |  0  0  0  0  2   3   1   3   1   1   2  0 | 0  1  3  2
.. .. ox .. .. ..&#x & |   3 |   0    1    2 |   *    *   *   *    * 2520 |  0   0   0   0   0   0   0   0    1    2    0   1   2 |  0   0   0   0  0  0   1   1   0   4    2   2   3 |  0  0  0  0  3   2   1   1   0   3   2  1 | 0  2  3  1
-----------------------+-----+---------------+----------------------------+-------------------------------------------------------+---------------------------------------------------+-------------------------------------------+-----------
x.3o.3o. .. .. ..    & ♦   4 |   6    0    0 |   4    0   0   0    0    0 | 70   *   *   *   *   *   *   *    *    *    *   *   * |  3   0   0   0  0  0   3   0   0   0    0   0   0 |  3  0  0  0  6   3   0   0   0   0   0  0 | 1  3  3  1
x.3o. .. x. .. ..    & ♦   6 |   6    3    0 |   2    3   0   0    0    0 |  * 420   *   *   *   *   *   *    *    *    *   *   * |  1   1   0   0  0  0   0   2   0   0    0   0   0 |  2  1  0  0  2   0   2   1   0   0   0  0 | 1  2  1  1
x. .. o.3x. .. ..    & ♦   6 |   3    6    0 |   0    3   2   0    0    0 |  *   * 420   *   *   *   *   *    *    *    *   *   * |  1   0   2   0  0  0   0   0   0   2    0   0   0 |  2  0  1  0  2   0   0   0   0   2   1  0 | 1  2  2  0
x. .. .. x.3o. ..    & ♦   6 |   3    6    0 |   0    3   0   2    0    0 |  *   *   * 840   *   *   *   *    *    *    *   *   * |  0   1   1   1  0  0   0   0   0   0    0   1   0 |  1  1  1  0  0   1   1   0   0   1   0  0 | 1  1  1  1
.. o.3o.3x. .. ..    & ♦   4 |   0    6    0 |   0    0   4   0    0    0 |  *   *   *   * 210   *   *   *    *    *    *   *   * |  1   0   0   0  2  0   0   0   0   0    0   0   2 |  2  0  0  1  2   0   0   0   0   1   0  2 | 1  3  1  0
.. .. o.3x.3o. ..    & ♦   6 |   0   12    0 |   0    0   4   4    0    0 |  *   *   *   *   * 420   *   *    *    *    *   *   * |  0   0   1   0  1  1   0   0   0   0    0   0   1 |  1  0  1  1  1   0   0   0   0   1   0  1 | 1  2  1  0
.. .. .. x.3o.3o.    & ♦   4 |   0    6    0 |   0    0   0   4    0    0 |  *   *   *   *   *   * 210   *    *    *    *   *   * |  0   0   0   2  0  2   1   0   0   0    0   0   0 |  0  1  2  1  2   2   0   0   0   0   0  0 | 1  1  2  1
xo3oo .. .. .. ..&#x & ♦   4 |   3    0    3 |   1    0   0   0    3    0 |  *   *   *   *   *   *   * 840    *    *    *   *   * |  0   0   0   0  0  0   1   2   2   0    0   0   0 |  0  0  0  0  2   2   1   2   1   0   0  0 | 0  1  2  2
xo .. ox .. .. ..&#x & ♦   4 |   1    1    4 |   0    0   0   0    2    2 |  *   *   *   *   *   *   *   * 1260    *    *   *   * |  0   0   0   0  0  0   1   0   0   2    2   0   0 |  0  0  0  0  2   2   0   1   0   1   2  0 | 0  1  3  1
xo .. .. xo .. ..&#x & ♦   5 |   2    2    4 |   0    1   0   0    2    2 |  *   *   *   *   *   *   *   *    * 2520    *   *   * |  0   0   0   0  0  0   0   1   0   1    1   1   0 |  0  0  0  0  1   1   1   1   0   1   1  0 | 0  1  2  1
xo .. .. .. .. ox&#x   ♦   4 |   2    0    4 |   0    0   0   0    4    0 |  *   *   *   *   *   *   *   *    *    * 1260   *   * |  0   0   0   0  0  0   0   0   2   0    2   0   0 |  0  0  0  0  0   2   0   2   1   0   1  0 | 0  0  2  2
.. oo3ox .. .. ..&#x & ♦   4 |   0    3    3 |   0    0   0   1    0    3 |  *   *   *   *   *   *   *   *    *    *    * 840   * |  0   0   0   0  0  0   1   0   0   0    0   2   2 |  0  0  0  0  2   2   1   0   0   2   0  1 | 0  2  2  1
.. .. ox3xo .. ..&#x   ♦   6 |   0    6    6 |   0    0   2   0    0    6 |  *   *   *   *   *   *   *   *    *    *    *   * 840 |  0   0   0   0  0  0   0   0   0   2    0   0   2 |  0  0  0  0  2   0   0   0   0   2   1  1 | 0  2  2  0
-----------------------+-----+---------------+----------------------------+-------------------------------------------------------+---------------------------------------------------+-------------------------------------------+-----------
x.3o.3o.3x. .. ..    & ♦  20 |  30   30    0 |  20   30  20   0    0    0 |  5  10  10   0   5   0   0   0    0    0    0   0   0 | 42   *   *   *  *  *   *   *   *   *    *   *   * |  2  0  0  0  2   0   0   0   0   0   0  0 | 1  2  1  0
x.3o. .. x.3o. ..    & ♦   9 |   9    9    0 |   3    9   0   3    0    0 |  0   3   0   3   0   0   0   0    0    0    0   0   0 |  * 280   *   *  *  *   *   *   *   *    *   *   * |  1  1  0  0  0   0   1   0   0   0   0  0 | 1  1  0  1
x. .. o.3x.3o. ..    & ♦  12 |   6   24    0 |   0   12   8   8    0    0 |  0   0   4   4   0   2   0   0    0    0    0   0   0 |  *   * 210   *  *  *   *   *   *   *    *   *   * |  1  0  1  0  0   0   0   0   0   1   0  0 | 1  1  1  0
x. .. .. x.3o.3o.    & ♦   8 |   4   12    0 |   0    6   0   8    0    0 |  0   0   0   4   0   0   2   0    0    0    0   0   0 |  *   *   * 210  *  *   *   *   *   *    *   *   * |  0  1  1  0  0   1   0   0   0   0   0  0 | 1  0  1  1
.. o.3o.3x.3o. ..    & ♦  10 |   0   30    0 |   0    0  20  10    0    0 |  0   0   0   0   5   5   0   0    0    0    0   0   0 |  *   *   *   * 84  *   *   *   *   *    *   *   * |  1  0  0  1  0   0   0   0   0   0   0  1 | 1  2  0  0
.. .. o.3x.3o.3o.    & ♦  10 |   0   30    0 |   0    0  10  20    0    0 |  0   0   0   0   0   5   5   0    0    0    0   0   0 |  *   *   *   *  * 84   *   *   *   *    *   *   * |  0  0  1  1  1   0   0   0   0   0   0  0 | 1  1  1  0
xo3oo3ox .. .. ..&#x & ♦   8 |   6    6   12 |   4    0   0   4   12   12 |  1   0   0   0   0   0   1   4    6    0    0   4   0 |  *   *   *   *  *  * 210   *   *   *    *   *   * |  0  0  0  0  2   2   0   0   0   0   0  0 | 0  1  2  1
xo3oo .. xo .. ..&#x & ♦   7 |   6    3    6 |   2    3   0   0    6    3 |  0   1   0   0   0   0   0   2    0    3    0   0   0 |  *   *   *   *  *  *   * 840   *   *    *   *   * |  0  0  0  0  1   0   1   1   0   0   0  0 | 0  1  1  1
xo3oo .. .. .. ox&#x & ♦   5 |   4    0    6 |   1    0   0   0    9    0 |  0   0   0   0   0   0   0   2    0    0    3   0   0 |  *   *   *   *  *  *   *   * 840   *    *   *   * |  0  0  0  0  0   1   0   1   1   0   0  0 | 0  0  1  2
xo .. ox3xo .. ..&#x & ♦   9 |   3    9   12 |   0    3   2   1    6   12 |  0   0   1   0   0   0   0   0    3    3    0   0   2 |  *   *   *   *  *  *   *   *   * 840    *   *   * |  0  0  0  0  1   0   0   0   0   1   1  0 | 0  1  2  0
xo .. ox .. .. ox&#x & ♦   6 |   3    2    8 |   0    1   0   0    8    4 |  0   0   0   0   0   0   0   0    2    2    2   0   0 |  *   *   *   *  *  *   *   *   *   * 1260   *   * |  0  0  0  0  0   1   0   1   0   0   1  0 | 0  0  2  1
xo .. .. xo3oo ..&#x & ♦   7 |   3    6    6 |   0    3   0   2    3    6 |  0   0   0   1   0   0   0   0    0    3    0   2   0 |  *   *   *   *  *  *   *   *   *   *    * 840   * |  0  0  0  0  0   1   1   0   0   1   0  0 | 0  1  1  1
.. oo3ox3xo .. ..&#x & ♦  10 |   0   18   12 |   0    0   8   4    0   18 |  0   0   0   0   1   1   0   0    0    0    0   4   4 |  *   *   *   *  *  *   *   *   *   *    *   * 420 |  0  0  0  0  1   0   0   0   0   1   0  1 | 0  2  1  0
-----------------------+-----+---------------+----------------------------+-------------------------------------------------------+---------------------------------------------------+-------------------------------------------+-----------
x.3o.3o.3x.3o. ..    & ♦  60 |  90  180    0 |  60  180 120  60    0    0 | 15  60  60  60  30  30   0   0    0    0    0   0   0 |  6  20  15   0  6  0   0   0   0   0    0   0   0 | 14  *  *  *  *   *   *   *   *   *   *  * | 1  1  0  0
x.3o. .. x.3o.3o.    & ♦  12 |  12   18    0 |   4   18   0  12    0    0 |  0   6   0  12   0   0   3   0    0    0    0   0   0 |  0   4   0   3  0  0   0   0   0   0    0   0   0 |  * 70  *  *  *   *   *   *   *   *   *  * | 1  0  0  1
x. .. o.3x.3o.3o.    & ♦  20 |  10   60    0 |   0   30  20  40    0    0 |  0   0  10  20   0  10  10   0    0    0    0   0   0 |  0   0   5   5  0  2   0   0   0   0    0   0   0 |  *  * 42  *  *   *   *   *   *   *   *  * | 1  0  1  0
.. o.3o.3x.3o.3o.    & ♦  20 |   0   90    0 |   0    0  60  60    0    0 |  0   0   0   0  15  30  15   0    0    0    0   0   0 |  0   0   0   0  6  6   0   0   0   0    0   0   0 |  *  *  * 14  *   *   *   *   *   *   *  * | 1  1  0  0
xo3oo3ox3xo .. ..&#x & ♦  30 |  30   60   60 |  20   30  20  30   60   90 |  5  10  10   0   5   5   5  20   30   30    0  20  20 |  1   0   0   0  0  1   5  10   0  10    0   0   5 |  *  *  *  * 84   *   *   *   *   *   *  * | 0  1  1  0
xo3oo3ox .. .. ox&#x & ♦  12 |  10   12   24 |   4    6   0   8   36   24 |  1   0   0   4   0   0   2   8   12   12   12   8   0 |  0   0   0   1  0  0   2   0   4   0    6   4   0 |  *  *  *  *  * 210   *   *   *   *   *  * | 0  0  1  1
xo3oo .. xo3oo ..&#x & ♦  10 |   9    9    9 |   3    9   0   3    9    9 |  0   3   0   3   0   0   0   3    0    9    0   3   0 |  0   1   0   0  0  0   0   3   0   0    0   3   0 |  *  *  *  *  *   * 280   *   *   *   *  * | 0  1  0  1
xo3oo .. xo .. ox&#x & ♦   8 |   7    3   12 |   2    3   0   0   18    6 |  0   1   0   0   0   0   0   4    3    6    6   0   0 |  0   0   0   0  0  0   0   2   2   0    3   0   0 |  *  *  *  *  *   *   * 420   *   *   *  * | 0  0  1  1
xo3oo .. .. oo3ox&#x   ♦   6 |   6    0    9 |   2    0   0   0   18    0 |  0   0   0   0   0   0   0   6    0    0    9   0   0 |  0   0   0   0  0  0   0   0   6   0    0   0   0 |  *  *  *  *  *   *   *   * 140   *   *  * | 0  0  0  2
xo .. ox3xo3oo ..&#x & ♦  16 |   6   30   24 |   0   12  12   8   12   36 |  0   0   4   4   1   2   0   0    6   12    0   8   8 |  0   0   1   0  0  0   0   0   0   4    0   4   2 |  *  *  *  *  *   *   *   *   * 210   *  * | 0  1  1  0
xo .. ox3xo .. ox&#x   ♦  12 |   6   12   24 |   0    6   4   0   24   24 |  0   0   2   0   0   0   0   0   12   12    6   0   4 |  0   0   0   0  0  0   0   0   0   4    6   0   0 |  *  *  *  *  *   *   *   *   *   * 210  * | 0  0  2  0
.. oo3ox3xo3oo ..&#x   ♦  20 |   0   60   30 |   0    0  40  20    0   60 |  0   0   0   0  10  10   0   0    0    0    0  20  20 |  0   0   0   0  2  0   0   0   0   0    0   0  10 |  *  *  *  *  *   *   *   *   *   *   * 42 | 0  2  0  0
-----------------------+-----+---------------+----------------------------+-------------------------------------------------------+---------------------------------------------------+-------------------------------------------+-----------
x.3o.3o.3x.3o.3o.    & ♦ 140 | 210  630    0 | 140  630 420 420    0    0 | 35 210 210 420 105 210 105   0    0    0    0   0   0 | 21 140 105 105 42 42   0   0   0   0    0   0   0 |  7 35 21  7  0   0   0   0   0   0   0  0 | 2  *  *  *
xo3oo3ox3xo3oo ..&#x & ♦  80 |  90  270  180 |  60  180 180 120  180  360 | 15  60  60  60  45  60  15  60   90  180    0 120 120 |  6  20  15   0 12  6  15  60   0  60    0  60  60 |  1  0  0  1  6   0  20   0   0  15   0  6 | * 14  *  *
xo3oo3ox3xo .. ox&#x & ♦  40 |  40   90  120 |  20   60  40  40  180  180 |  5  10  20  20   5  10  10  40   90  120   60  40  40 |  1   0   5   5  0  2  10  20  20  40   60  20  10 |  0  0  1  0  2   5   0  10   0   5  10  0 | *  * 42  *
xo3oo3ox .. oo3ox&#x & ♦  16 |  18   18   36 |   8   18   0  12   72   36 |  1   6   0  12   0   0   3  24   18   36   36  12   0 |  0   4   0   3  0  0   3  12  24   0   18  12   0 |  0  1  0  0  0   3   4   6   4   0   0  0 | *  *  * 70
```