Acronym	tetrap
Name	tetrahedron - rectified-pentachoron duoprism, vertex figure of torfy
Circumradius	sqrt(39/40) = 0.987421
Volume	11 sqrt(10)/1152 = 0.030195
Face vector	40, 180, 340, 350, 214, 76, 14
Confer	general polytopal classes: Wythoffian polyexa
External links

Incidence matrix according to Dynkin symbol

x3o3o o3x3o3o

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