Acronym trapendafup
Name triangular-pentachoron duoantifastegiaprism,
trapen atop bidual trapen
Circumradius sqrt(3)/2 = 0.866025
Confer
general polytopal classes:
scaliform   segmentoexa  

Incidence matrix according to Dynkin symbol

xo3ox xo3oo3oo3ox&#x   → height = 1/sqrt(15) = 0.258199
(trapen || bidual trapen)

o.3o. o.3o.3o.3o.    & | 30 |  2  4   8 |  1  8  6  12  36 |  4 12  4  4  30  24  32  24 |  6  8 1 18  28  36  20 10  20 |  4 2 16 12  9 16 14  6 2 | 1  5 10 3
-----------------------+----+-----------+------------------+-----------------------------+-------------------------------+--------------------------+----------
x. .. .. .. .. ..    & |  2 | 30  *   * |  1  4  0   4   0 |  4  6  0  4  12   6   0   0 |  6  4 0 18  12  12   4  0   0 |  4 1 16 12  4  6  4  1 0 | 1  5 10 1
.. .. x. .. .. ..    & |  2 |  * 60   * |  0  2  3   0   6 |  1  6  3  0   6   3  12   6 |  3  6 1  3  12   9   6  6   8 |  3 2  6  3  6  7  5  3 2 | 1  3  4 3
oo3oo oo3oo3oo3oo&#x   |  2 |  *  * 120 |  0  0  0   2   6 |  0  0  0  1   6   6   6   6 |  0  0 0  6   6  12   6  2   6 |  0 0  6  6  2  6  6  2 1 | 0  2  6 2
-----------------------+----+-----------+------------------+-----------------------------+-------------------------------+--------------------------+----------
x.3o. .. .. .. ..    & |  3 |  3  0   0 | 10  *  *   *   * |  4  0  0  4   0   0   0   0 |  6  0 0 18   0   0   0  0   0 |  4 0 16 12  0  0  0  0 0 | 1  5 10 0
x. .. x. .. .. ..    & |  4 |  2  2   0 |  * 60  *   *   * |  1  3  0  0   3   0   0   0 |  3  3 0  3   6   3   0  0   0 |  3 1  6  3  3  3  1  0 0 | 1  3  4 1
.. .. x.3o. .. ..    & |  3 |  0  3   0 |  *  * 60   *   * |  0  2  2  0   0   0   4   0 |  1  4 1  0   4   0   2  4   2 |  2 2  2  0  4  2  1  2 2 | 1  2  1 3
xo .. .. .. .. ..&#x & |  3 |  1  0   2 |  *  *  * 120   * |  0  0  0  1   3   3   0   0 |  0  0 0  6   3   6   3  0   0 |  0 0  6  6  1  3  3  1 0 | 0  2  6 1
.. .. xo .. .. ..&#x & |  3 |  0  1   2 |  *  *  *   * 360 |  0  0  0  0   1   1   2   2 |  0  0 0  1   2   4   2  1   3 |  0 0  2  2  1  3  3  1 1 | 0  1  3 2
-----------------------+----+-----------+------------------+-----------------------------+-------------------------------+--------------------------+----------
x.3o. x. .. .. ..    &   6 |  6  3   0 |  2  3  0   0   0 | 20  *  *  *   *   *   *   * |  3  0 0  3   0   0   0  0   0 |  3 0  6  3  0  0  0  0 0 | 1  3  4 0
x. .. x.3o. .. ..    &   6 |  3  6   0 |  0  3  2   0   0 |  * 60  *  *   *   *   *   * |  1  2 0  0   2   0   0  0   0 |  2 1  2  0  2  1  0  0 0 | 1  2  1 1
.. .. x.3o.3o. ..    &   4 |  0  6   0 |  0  0  4   0   0 |  *  * 30  *   *   *   *   * |  0  2 1  0   0   0   0  2   0 |  1 2  0  0  2  0  0  1 2 | 1  1  0 3
xo3ox .. .. .. ..&#x     6 |  6  0   6 |  2  0  0   6   0 |  *  *  * 20   *   *   *   * |  0  0 0  6   0   0   0  0   0 |  0 0  6  6  0  0  0  0 0 | 0  2  6 0
xo .. xo .. .. ..&#x &   5 |  2  2   4 |  0  1  0   2   2 |  *  *  *  * 180   *   *   * |  0  0 0  1   2   2   0  0   0 |  0 0  2  2  1  2  1  0 0 | 0  1  3 1
xo .. .. .. .. ox&#x &   4 |  1  1   4 |  0  0  0   2   2 |  *  *  *  *   * 180   *   * |  0  0 0  1   0   2   2  0   0 |  0 0  2  2  0  1  2  1 0 | 0  1  3 1
.. .. xo3oo .. ..&#x &   4 |  0  3   3 |  0  0  1   0   3 |  *  *  *  *   *   * 240   * |  0  0 0  0   1   0   1  1   1 |  0 0  1  0  1  1  1  1 1 | 0  1  1 2
.. .. xo .. .. ox&#x     4 |  0  2   4 |  0  0  0   0   4 |  *  *  *  *   *   *   * 180 |  0  0 0  0   0   2   0  0   2 |  0 0  0  1  0  2  2  0 1 | 0  0  2 2
-----------------------+----+-----------+------------------+-----------------------------+-------------------------------+--------------------------+----------
x.3o. x.3o. .. ..    &   9 |  9  9   0 |  3  9  3   0   0 |  3  3  0  0   0   0   0   0 | 20  * *  *   *   *   *  *   * |  2 0  2  0  0  0  0  0 0 | 1  2  1 0
x. .. x.3o.3o. ..    &   8 |  4 12   0 |  0  6  8   0   0 |  0  4  2  0   0   0   0   0 |  * 30 *  *   *   *   *  *   * |  1 1  0  0  1  0  0  0 0 | 1  1  0 1
.. .. x.3o.3o.3o.    &   5 |  0 10   0 |  0  0 10   0   0 |  0  0  5  0   0   0   0   0 |  *  * 6  *   *   *   *  *   * |  0 2  0  0  0  0  0  0 2 | 1  0  0 3
xo3ox xo .. .. ..&#x &   9 |  9  3  12 |  3  3  0  12   6 |  1  0  0  2   3   3   0   0 |  *  * * 60   *   *   *  *   * |  0 0  2  2  0  0  0  0 0 | 0  1  3 0
xo .. xo3oo .. ..&#x &   7 |  3  6   6 |  0  3  2   3   6 |  0  1  0  0   3   0   2   0 |  *  * *  * 120   *   *  *   * |  0 0  1  0  1  1  0  0 0 | 0  1  1 1
xo .. xo .. .. ox&#x &   6 |  2  3   8 |  0  1  0   4   8 |  0  0  0  0   2   2   0   2 |  *  * *  *   * 180   *  *   * |  0 0  0  1  0  1  1  0 0 | 0  0  2 1
xo .. .. .. oo3ox&#x &   5 |  1  3   6 |  0  0  1   3   6 |  0  0  0  0   0   3   2   0 |  *  * *  *   *   * 120  *   * |  0 0  1  0  0  0  1  1 0 | 0  1  1 1
.. .. xo3oo3oo ..&#x &   5 |  0  6   4 |  0  0  4   0   6 |  0  0  1  0   0   0   4   0 |  *  * *  *   *   *   * 60   * |  0 0  0  0  1  0  0  1 1 | 0  1  0 2
.. .. xo3oo .. ox&#x &   5 |  0  4   6 |  0  0  1   0   9 |  0  0  0  0   0   0   2   3 |  *  * *  *   *   *   *  * 120 |  0 0  0  0  0  1  1  0 1 | 0  0  1 2
-----------------------+----+-----------+------------------+-----------------------------+-------------------------------+--------------------------+----------
x.3o. x.3o.3o. ..    &  12 | 12 18   0 |  4 18 12   0   0 |  6 12  3  0   0   0   0   0 |  4  3 0  0   0   0   0  0   0 | 10 *  *  *  *  *  *  * * | 1  1  0 0
x. .. x.3o.3o.3o.    &  10 |  5 20   0 |  0 10 20   0   0 |  0 10 10  0   0   0   0   0 |  0  5 2  0   0   0   0  0   0 |  * 6  *  *  *  *  *  * * | 1  0  0 1
xo3ox xo3oo .. ..&#x &  12 | 12  9  18 |  4  9  3  18  18 |  3  3  0  3   9   9   6   0 |  1  0 0  3   3   0   3  0   0 |  * * 40  *  *  *  *  * * | 0  1  1 0
xo3ox xo .. .. ox&#x    12 | 12  6  24 |  4  6  0  24  24 |  2  0  0  4  12  12   0   6 |  0  0 0  4   0   6   0  0   0 |  * *  * 30  *  *  *  * * | 0  0  2 0
xo .. xo3oo3oo ..&#x &   9 |  4 12   8 |  0  6  8   4  12 |  0  4  2  0   6   0   8   0 |  0  1 0  0   4   0   0  2   0 |  * *  *  * 30  *  *  * * | 0  1  0 1
xo .. xo3oo .. ox&#x &   8 |  3  7  12 |  0  3  2   6  18 |  0  1  0  0   6   3   4   6 |  0  0 0  0   2   3   0  0   2 |  * *  *  *  * 60  *  * * | 0  0  1 1
xo .. xo .. oo3ox&#x &   7 |  2  5  12 |  0  1  1   6  18 |  0  0  0  0   3   6   4   6 |  0  0 0  0   0   3   2  0   2 |  * *  *  *  *  * 60  * * | 0  0  1 1
xo .. .. oo3oo3ox&#x &   6 |  1  6   8 |  0  0  4   4  12 |  0  0  1  0   0   6   8   0 |  0  0 0  0   0   0   4  2   0 |  * *  *  *  *  *  * 30 * | 0  1  0 1
.. .. xo3oo3oo3ox&#x    10 |  0 20  20 |  0  0 20   0  60 |  0  0 10  0   0   0  40  30 |  0  0 2  0   0   0   0 10  20 |  * *  *  *  *  *  *  * 6 | 0  0  0 2
-----------------------+----+-----------+------------------+-----------------------------+-------------------------------+--------------------------+----------
x.3o. x.3o.3o.3o.    &  15 | 15 30   0 |  5 30 30   0   0 | 10 30 15  0   0   0   0   0 | 10 15 3  0   0   0   0  0   0 |  5 3  0  0  0  0  0  0 0 | 2  *  * *
xo3ox xo3oo3oo ..&#x &  15 | 15 18  24 |  5 18 12  24  36 |  6 12  3  4  18  18  24   0 |  4  3 0  6  12   0  12  6   0 |  1 0  4  0  3  0  0  3 0 | * 10  * *
xo3ox xo3oo .. ox&#x &  15 | 15 12  36 |  5 12  3  36  54 |  4  3  0  6  27  27  12  18 |  1  0 0  9   6  18   6  0   6 |  0 0  2  3  0  3  3  0 0 | *  * 20 *
xo .. xo3oo3oo3ox&#x &  15 |  5 30  40 |  0 10 30  20 120 |  0 10 15  0  30  30  80  60 |  0  5 3  0  20  30  20 20  40 |  0 1  0  0  5 10 10  5 2 | *  *  * 6

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