Acronym cograxa (old: cograxalcograx) Name cograx alterprism,cograx atop alternate cograx Circumradius sqrt(11/2) = 2.345208 Confer general polytopal classes: scaliform

Incidence matrix according to Dynkin symbol

```xx3xo3xx3ox3xx&#x   → height = 1/sqrt(3) = 0.577350
(cappix || alt. cappix)

o.3o.3o.3o.3o.     & | 720 |   1   1   2   2   2 |   1   2   2   2   2   1   2   1   4   3   2 |  2   2   1   2   1  1   2   1  1   3   4   3   2   3   1 |  1  2  1  1  1  3   2   3   3  2  1 | 1  2  3  1
---------------------+-----+---------------------+---------------------------------------------+----------------------------------------------------------+-------------------------------------+-----------
x. .. .. .. ..     & |   2 | 360   *   *   *   * |   1   2   2   0   0   0   0   0   2   0   0 |  2   2   1   2   1  0   0   0  0   2   2   1   2   0   0 |  1  2  1  1  0  2   1   3   1  2  0 | 1  1  3  1
.. x. .. .. ..     & |   2 |   * 360   *   *   * |   1   0   0   2   2   0   0   0   0   2   0 |  2   2   0   0   0  1   2   1  0   2   0   2   0   2   1 |  1  2  1  0  1  2   2   2   2  0  1 | 1  2  2  1
.. .. x. .. ..     & |   2 |   *   * 720   *   * |   0   1   0   1   0   1   1   0   0   0   1 |  1   0   1   1   0  1   1   0  1   0   2   0   0   2   0 |  1  1  0  1  1  2   0   0   2  1  1 | 1  2  2  0
.. .. .. .. x.     & |   2 |   *   *   * 720   * |   0   0   1   0   1   0   1   1   1   0   0 |  0   1   0   1   1  0   1   1  1   1   1   1   1   0   0 |  0  1  1  1  1  1   1   2   1  1  0 | 1  1  2  1
oo3oo3oo3oo3oo&#x    |   2 |   *   *   *   * 720 |   0   0   0   0   0   0   0   0   2   2   1 |  0   0   0   0   0  0   0   0  0   2   2   2   1   2   1 |  0  0  0  0  0  2   2   2   2  1  1 | 0  2  2  1
---------------------+-----+---------------------+---------------------------------------------+----------------------------------------------------------+-------------------------------------+-----------
x.3x. .. .. ..     & |   6 |   3   3   0   0   0 | 120   *   *   *   *   *   *   *   *   *   * |  2   2   0   0   0  0   0   0  0   2   0   0   0   0   0 |  1  2  1  0  0  2   1   2   0  0  0 | 1  1  2  1
x. .. x. .. ..     & |   4 |   2   0   2   0   0 |   * 360   *   *   *   *   *   *   *   *   * |  1   0   1   1   0  0   0   0  0   0   1   0   0   0   0 |  1  1  0  1  0  1   0   0   1  1  0 | 1  1  2  0
x. .. .. .. x.     & |   4 |   2   0   0   2   0 |   *   * 360   *   *   *   *   *   *   *   * |  0   1   0   1   1  0   0   0  0   0   0   0   1   0   0 |  0  1  1  1  0  0   0   2   0  1  0 | 1  0  2  1
.. x.3x. .. ..     & |   6 |   0   3   3   0   0 |   *   *   * 240   *   *   *   *   *   *   * |  1   0   0   0   0  1   1   0  0   0   0   0   0   0   0 |  1  1  0  0  1  1   0   0   1  0  1 | 1  2  1  0
.. x. .. .. x.     & |   4 |   0   2   0   2   0 |   *   *   *   * 360   *   *   *   *   *   * |  0   1   0   0   0  0   1   1  0   0   0   1   0   0   0 |  0  1  1  0  1  0   1   1   1  0  0 | 1  1  1  1
.. .. x.3o. ..     & |   3 |   0   0   3   0   0 |   *   *   *   *   * 240   *   *   *   *   * |  0   0   1   0   0  1   0   0  1   0   0   0   0   1   0 |  1  0  0  1  1  1   0   0   1  0  1 | 1  2  1  0
.. .. x. .. x.     & |   4 |   0   0   2   2   0 |   *   *   *   *   *   * 360   *   *   *   * |  0   0   0   1   0  0   1   0  1   0   1   0   0   0   0 |  0  1  0  1  1  1   0   0   1  1  0 | 1  1  2  0
.. .. .. o.3x.     & |   3 |   0   0   0   3   0 |   *   *   *   *   *   *   * 240   *   *   * |  0   0   0   0   1  0   0   1  1   1   0   0   0   0   0 |  0  0  1  1  1  1   1   1   0  0  0 | 1  1  1  1
xx .. .. .. ..&#x  & |   4 |   1   0   0   1   2 |   *   *   *   *   *   *   *   * 720   *   * |  0   0   0   0   0  0   0   0  0   1   1   1   1   0   0 |  0  0  0  0  0  1   1   2   1  1  0 | 0  1  2  1
.. xo .. .. ..&#x  & |   3 |   0   1   0   0   2 |   *   *   *   *   *   *   *   *   * 720   * |  0   0   0   0   0  0   0   0  0   1   0   1   0   1   1 |  0  0  0  0  0  1   2   1   1  0  1 | 0  2  1  1
.. .. xx .. ..&#x    |   4 |   0   0   2   0   2 |   *   *   *   *   *   *   *   *   *   * 360 |  0   0   0   0   0  0   0   0  0   0   2   0   0   2   0 |  0  0  0  0  0  2   0   0   2  1  1 | 0  2  2  0
---------------------+-----+---------------------+---------------------------------------------+----------------------------------------------------------+-------------------------------------+-----------
x.3x.3x. .. ..     & ♦  24 |  12  12  12   0   0 |   4   6   0   4   0   0   0   0   0   0   0 | 60   *   *   *   *  *   *   *  *   *   *   *   *   *   * |  1  1  0  0  0  1   0   0   0  0  0 | 1  1  1  0
x.3x. .. .. x.     & ♦  12 |   6   6   0   6   0 |   2   0   3   0   3   0   0   0   0   0   0 |  * 120   *   *   *  *   *   *  *   *   *   *   *   *   * |  0  1  1  0  0  0   0   1   0  0  0 | 1  0  1  1
x. .. x.3o. ..     & ♦   6 |   3   0   6   0   0 |   0   3   0   0   0   2   0   0   0   0   0 |  *   * 120   *   *  *   *   *  *   *   *   *   *   *   * |  1  0  0  1  0  0   0   0   1  0  0 | 1  1  1  0
x. .. x. .. x.     & ♦   8 |   4   0   4   4   0 |   0   2   2   0   0   0   2   0   0   0   0 |  *   *   * 180   *  *   *   *  *   *   *   *   *   *   * |  0  1  0  1  0  0   0   0   0  1  0 | 1  0  2  0
x. .. .. o.3x.     & ♦   6 |   3   0   0   6   0 |   0   0   3   0   0   0   0   2   0   0   0 |  *   *   *   * 120  *   *   *  *   *   *   *   *   *   * |  0  0  1  1  0  0   1   0   0  0  0 | 1  0  1  1
.. x.3x.3o. ..     & ♦  12 |   0   6  12   0   0 |   0   0   0   4   0   4   0   0   0   0   0 |  *   *   *   *   * 60   *   *  *   *   *   *   *   *   * |  1  0  0  0  1  0   0   0   0  0  1 | 1  2  0  0
.. x.3x. .. x.     & ♦  12 |   0   6   6   6   0 |   0   0   0   2   3   0   3   0   0   0   0 |  *   *   *   *   *  * 120   *  *   *   *   *   *   *   * |  0  1  0  0  1  0   0   0   1  0  0 | 1  1  1  0
.. x. .. o.3x.     & ♦   6 |   0   3   0   6   0 |   0   0   0   0   3   0   0   2   0   0   0 |  *   *   *   *   *  *   * 120  *   *   *   *   *   *   * |  0  0  1  0  1  0   1   0   0  0  0 | 1  1  0  1
.. .. x.3o.3x.     & ♦  12 |   0   0  12  12   0 |   0   0   0   0   0   4   6   4   0   0   0 |  *   *   *   *   *  *   *   * 60   *   *   *   *   *   * |  0  0  0  1  1  1   0   0   0  0  0 | 1  1  1  0
xx3xo .. .. ..&#x  & ♦   9 |   3   3   0   3   6 |   1   0   0   0   0   0   0   1   3   3   0 |  *   *   *   *   *  *   *   *  * 240   *   *   *   *   * |  0  0  0  0  0  1   1   1   0  0  0 | 0  1  1  1
xx .. xx .. ..&#x  & ♦   8 |   2   0   4   2   4 |   0   1   0   0   0   0   1   0   2   0   2 |  *   *   *   *   *  *   *   *  *   * 360   *   *   *   * |  0  0  0  0  0  1   0   0   1  1  0 | 0  1  2  0
xx .. .. ox ..&#x  & ♦   6 |   1   2   0   2   4 |   0   0   0   0   1   0   0   0   2   2   0 |  *   *   *   *   *  *   *   *  *   *   * 360   *   *   * |  0  0  0  0  0  0   1   1   1  0  0 | 0  1  1  1
xx .. .. .. xx&#x    ♦   8 |   4   0   0   4   4 |   0   0   2   0   0   0   0   0   4   0   0 |  *   *   *   *   *  *   *   *  *   *   *   * 180   *   * |  0  0  0  0  0  0   0   2   0  1  0 | 0  0  2  1
.. xo3xx .. ..&#x  & ♦   9 |   0   3   6   0   6 |   0   0   0   1   0   1   0   0   0   3   3 |  *   *   *   *   *  *   *   *  *   *   *   *   * 240   * |  0  0  0  0  0  1   0   0   1  0  1 | 0  2  1  0
.. xo .. ox ..&#x    ♦   4 |   0   2   0   0   4 |   0   0   0   0   0   0   0   0   0   4   0 |  *   *   *   *   *  *   *   *  *   *   *   *   *   * 180 |  0  0  0  0  0  0   2   0   0  0  1 | 0  2  0  1
---------------------+-----+---------------------+---------------------------------------------+----------------------------------------------------------+-------------------------------------+-----------
x.3x.3x.3o. ..     & ♦  60 |  30  30  60   0   0 |  10  30   0  20   0  20   0   0   0   0   0 |  5   0  10   0   0  5   0   0  0   0   0   0   0   0   0 | 12  *  *  *  *  *   *   *   *  *  * | 1  1  0  0
x.3x.3x. .. x.     & ♦  48 |  24  24  24  24   0 |   8  12  12   8  12   0  12   0   0   0   0 |  2   4   0   6   0  0   4   0  0   0   0   0   0   0   0 |  * 30  *  *  *  *   *   *   *  *  * | 1  0  1  0
x.3x. .. o.3x.     & ♦  18 |   9   9   0  18   0 |   3   0   9   0   9   0   0   6   0   0   0 |  0   3   0   0   3  0   0   3  0   0   0   0   0   0   0 |  *  * 40  *  *  *   *   *   *  *  * | 1  0  0  1
x. .. x.3o.3x.     & ♦  24 |  12   0  24  24   0 |   0  12  12   0   0   8  12   8   0   0   0 |  0   0   4   6   4  0   0   0  2   0   0   0   0   0   0 |  *  *  * 30  *  *   *   *   *  *  * | 1  0  1  0
.. x.3x.3o.3x.     & ♦  60 |   0  30  60  60   0 |   0   0   0  20  30  20  30  20   0   0   0 |  0   0   0   0   0  5  10  10  5   0   0   0   0   0   0 |  *  *  *  * 12  *   *   *   *  *  * | 1  1  0  0
xx3xo3xx .. ..&#x  & ♦  36 |  12  12  24  12  24 |   4   6   0   4   0   4   6   4  12  12  12 |  1   0   0   0   0  0   0   0  1   4   6   0   0   4   0 |  *  *  *  *  * 60   *   *   *  *  * | 0  1  1  0
xx3xo .. ox ..&#x  & ♦  12 |   3   6   0   6  12 |   1   0   0   0   3   0   0   2   6  12   0 |  0   0   0   0   0  0   0   1  0   2   0   3   0   0   3 |  *  *  *  *  *  * 120   *   *  *  * | 0  1  0  1
xx3xo .. .. xx&#x  & ♦  18 |   9   6   0  12  12 |   2   0   6   0   3   0   0   2  12   6   0 |  0   1   0   0   1  0   0   0  0   2   0   3   3   0   0 |  *  *  *  *  *  *   * 120   *  *  * | 0  0  1  1
xx .. xx3ox ..&#x  & ♦  18 |   3   6  12   6  12 |   0   3   0   2   3   2   3   0   6   6   6 |  0   0   1   0   0  0   1   0  0   0   3   3   0   2   0 |  *  *  *  *  *  *   *   * 120  *  * | 0  1  1  0
xx .. xx .. xx&#x    ♦  16 |   8   0   8   8   8 |   0   4   4   0   0   0   4   0   8   0   4 |  0   0   0   2   0  0   0   0  0   0   4   0   2   0   0 |  *  *  *  *  *  *   *   *   * 90  * | 0  0  2  0
.. xo3xx3ox ..&#x    ♦  24 |   0  12  24   0  24 |   0   0   0   8   0   8   0   0   0  24  12 |  0   0   0   0   0  2   0   0  0   0   0   0   0   8   6 |  *  *  *  *  *  *   *   *   *  * 30 | 0  2  0  0
---------------------+-----+---------------------+---------------------------------------------+----------------------------------------------------------+-------------------------------------+-----------
x.3x.3x.3o.3x.     & ♦ 360 | 180 180 360 360   0 |  60 180 180 120 180 120 180 120   0   0   0 | 30  60  60  90  60 30  60  60 30   0   0   0   0   0   0 |  6 15 20 15  6  0   0   0   0  0  0 | 2  *  *  *
xx3xo3xx3ox ..&#x  & ♦ 120 |  30  60 120  60 120 |  10  30   0  40  30  40  30  20  60 120  60 |  5   0  10   0   0 10  10  10  5  20  30  30   0  40  30 |  1  0  0  0  1  5  10   0  10  0  5 | * 12  *  *
xx3xo3xx .. xx&#x  & ♦  72 |  36  24  48  48  48 |   8  24  24   8  12   8  24   8  48  24  24 |  2   4   4  12   4  0   4   0  2   8  24  12  12   8   0 |  0  1  0  1  0  2   0   4   4  6  0 | *  * 30  *
xx3xo .. ox3xx&#x    ♦  36 |  18  18   0  36  36 |   6   0  18   0  18   0   0  12  36  36   0 |  0   6   0   0   6  0   0   6  0  12   0  18   9   0   9 |  0  0  2  0  0  0   6   6   0  0  0 | *  *  * 20
```