Acronym penrap
Name (pentachoron, rectified pentachoron)-duoprism
Circumradius 1
Volume 55/9216 = 0.0059679
Confer
uniform relative:
fy  
general polytopal classes:
segmentozetta  

Incidence matrix according to Dynkin symbol

x3o3o3o o3x3o3o

. . . . . . . . | 50 |   4   6 |   6  24  3   6 |  4  36  12  24  3  2 |  1  24  18  36 12  8 1 |  6 12  24 18 12  4 |  3  6 12  8  6 | 3 2 4
----------------+----+---------+----------------+----------------------+------------------------+--------------------+----------------+------
x . . . . . . . |  2 | 100   * |   3   6  0   0 |  3  18   3   6  0  0 |  1  18   9  18  3  2 0 |  6  9  18  9  6  1 |  3  6  9  6  3 | 3 2 3
. . . . . x . . |  2 |   * 150 |   0   4  1   2 |  0   6   4   8  2  1 |  0   4   6  12  8  4 1 |  1  4   8 12  6  4 |  1  2  8  4  6 | 2 1 4
----------------+----+---------+----------------+----------------------+------------------------+--------------------+----------------+------
x3o . . . . . . |  3 |   3   0 | 100   *  *   * |  2   6   0   0  0  0 |  1  12   3   6  0  0 0 |  6  6  12  3  2  0 |  3  6  6  4  1 | 3 2 2
x . . . . x . . |  4 |   2   2 |   * 300  *   * |  0   3   1   2  0  0 |  0   3   3   6  2  1 0 |  1  6  12 12  6  1 |  1  2  6  3  3 | 2 1 3
. . . . o3x . . |  3 |   0   3 |   *   * 50   * |  0   0   4   0  2  0 |  0   0   6   0  8  0 1 |  0  4   0 12  0  4 |  1  0  2  0  6 | 2 0 4
. . . . . x3o . |  3 |   0   3 |   *   *  * 100 |  0   0   0   4  1  1 |  0   0   0   6  4  4 1 |  0  0   4  6  6  4 |  0  1  4  4  6 | 1 1 4
----------------+----+---------+----------------+----------------------+------------------------+--------------------+----------------+------
x3o3o . . . . .   4 |   6   0 |   4   0  0   0 | 50   *   *   *  *  * |  1   6   0   0  0  0 0 |  6  3   6  0  0  0 |  3  6  3  2  0 | 3 2 1
x3o . . . x . .   6 |   6   3 |   2   3  0   0 |  * 300   *   *  *  * |  0   2   1   2  0  0 0 |  1  2   4  2  1  0 |  1  2  6  2  1 | 2 1 2
x . . . o3x . .   6 |   3   6 |   0   3  2   0 |  *   * 100   *  *  * |  0   0   3   0  2  0 0 |  0  3   0  6  0  1 |  1  0  6  0  3 | 2 0 3
x . . . . x3o .   6 |   3   6 |   0   3  0   2 |  *   *   * 200  *  * |  0   0   0   3  1  1 0 |  0  0   3  3  3  1 |  0  1  3  3  3 | 1 1 3
. . . . o3x3o .   6 |   0  12 |   0   0  4   4 |  *   *   *   * 25  * |  0   0   0   0  4  0 1 |  0  0   0  6  0  4 |  0  0  4  0  6 | 1 0 4
. . . . . x3o3o   4 |   0   6 |   0   0  0   4 |  *   *   *   *  * 25 |  0   0   0   0  0  4 1 |  0  0   0  0  6  4 |  0  0  0  4  6 | 0 1 4
----------------+----+---------+----------------+----------------------+------------------------+--------------------+----------------+------
x3o3o3o . . . .   5 |  10   0 |  10   0  0   0 |  5   0   0   0  0  0 | 10   *   *   *  *  * * |  6  0   0  0  0  0 |  3  6  0  0  0 | 3 2 0
x3o3o . . x . .   8 |  12   4 |   8   6  0   0 |  2   4   0   0  0  0 |  * 150   *   *  *  * * |  1  1   2  0  0  0 |  1  2  2  1  0 | 2 1 1
x3o . . o3x . .   9 |   9   9 |   3   9  3   0 |  0   3   3   0  0  0 |  *   * 100   *  *  * * |  0  2   0  2  0  0 |  1  0  4  0  1 | 2 0 2
x3o . . . x3o .   9 |   9   9 |   3   9  0   3 |  0   3   0   3  0  0 |  *   *   * 200  *  * * |  0  0   2  1  1  0 |  0  1  2  2  1 | 1 1 2
x . . . o3x3o .  12 |   6  24 |   0  12  8   8 |  0   0   4   4  2  0 |  *   *   *   * 50  * * |  0  0   0  3  0  1 |  0  0  3  0  3 | 1 0 3
x . . . . x3o3o   8 |   4  12 |   0   6  0   8 |  0   0   0   4  0  2 |  *   *   *   *  * 50 * |  0  0   0  0  3  1 |  0  0  0  3  3 | 0 1 3
. . . . o3x3o3o  10 |   0  30 |   0   0 10  20 |  0   0   0   0  5  5 |  *   *   *   *  *  * 5   0  0   0  0  0  4 |  0  0  0  0  6 | 0 0 4
----------------+----+---------+----------------+----------------------+------------------------+--------------------+----------------+------
x3o3o3o . x . .  10 |  20   5 |  20  10  0   0 | 10  10   0   0  0  0 |  2   5   0   0  0  0 0 | 30  *   *  *  *  * |  1  2  0  0  0 | 2 1 0
x3o3o . o3x . .  12 |  18  12 |  12  18  4   0 |  3  12   6   0  0  0 |  0   3   4   0  0  0 0 |  * 50   *  *  *  * |  1  0  2  0  0 | 2 0 1
x3o3o . . x3o .  12 |  18  12 |  12  18  0   4 |  3  12   0   6  0  0 |  0   3   0   4  0  0 0 |  *  * 100  *  *  * |  0  1  1  1  0 | 1 1 1
x3o . . o3x3o .  18 |  18  36 |   6  36 12  12 |  0  12  12  12  3  0 |  0   0   4   4  3  0 0 |  *  *   * 50  *  * |  0  0  2  0  1 | 1 0 2
x3o . . . x3o3o  12 |  12  18 |   4  18  0  12 |  0   6   0  12  0  3 |  0   0   0   4  0  3 0 |  *  *   *  * 50  * |  0  0  0  2  1 | 0 1 2
x . . . o3x3o3o  20 |  10  60 |   0  30 20  40 |  0   0  10  20 10 10 |  0   0   0   0  5  5 2 |  *  *   *  *  * 10 |  0  0  0  0  3 | 0 0 3
----------------+----+---------+----------------+----------------------+------------------------+--------------------+----------------+------
x3o3o3o o3x . .  15 |  30  15 |  30  30  5   0 | 15  30  10   0  0  0 |  3  15  10   0  0  0 0 |  3  5   0  0  0  0 | 10  *  *  *  * | 2 0 0
x3o3o3o . x3o .  15 |  30  15 |  30  30  0   5 | 15  30   0  10  0  0 |  3  15   0  10  0  0 0 |  3  0   5  0  0  0 |  * 20  *  *  * | 1 1 0
x3o3o . o3x3o .  24 |  36  48 |  24  72 16  16 |  6  72  24  24  4  0 |  0  12  16  16  6  0 0 |  0  4   4  4  0  0 |  *  * 25  *  * | 1 0 1
x3o3o . . x3o3o  16 |  24  24 |  16  36  0  16 |  4  24   0  24  0  4 |  0   6   0  16  0  6 0 |  0  0   4  0  4  0 |  *  *  * 25  * | 0 1 1
x3o . . o3x3o3o  30 |  30  90 |  10  90 30  60 |  0  30  30  60 15 15 |  0   0  10  20 15 15 3 |  0  0   0  5  5  3 |  *  *  *  * 10 | 0 0 2
----------------+----+---------+----------------+----------------------+------------------------+--------------------+----------------+------
x3o3o3o o3x3o .  30 |  60  60 |  60 120 20  20 | 30 120  40  40  5  0 |  6  60  40  40 10  0 0 | 12 20  20 10  0  0 |  4  4  5  0  0 | 5 * *
x3o3o3o . x3o3o  20 |  40  30 |  40  60  0  20 | 20  60   0  40  0  5 |  4  30   0  40  0 10 0 |  6  0  20  0 10  0 |  0  4  0  5  0 | * 5 *
x3o3o . o3x3o3o  40 |  60 120 |  40 180 40  80 | 10 120  60 120 20 20 |  0  30  40  80 30 30 4 |  0 10  20 20 20  6 |  0  0  5  5  4 | * * 5

ox3oo3oo oo3xx3oo3oo&#x   → height = sqrt(5/8) = 0.790569

... 

xo ox3oo oo3xx3oo3oo&#x   → height = sqrt(5/12) = 0.645497

... 

xo3ox3oo xx3oo3oo3oo&#x   → height = sqrt(5/8) = 0.790569

... 

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