Acronym tetdip
Name tetrahedron-tetrahedron duoprism
Circumradius sqrt(3)/2 = 0.866025

Incidence matrix according to Dynkin symbol

x3o3o x3o3o

. . . . . . | 16 |  3  3 |  3  9  3 | 1  9  9 1 | 3  9 3 | 3 3
------------+----+-------+----------+-----------+--------+----
x . . . . . |  2 | 24  * |  2  3  0 | 1  6  3 0 | 3  6 1 | 3 2
. . . x . . |  2 |  * 24 |  0  3  2 | 0  3  6 1 | 1  6 3 | 2 3
------------+----+-------+----------+-----------+--------+----
x3o . . . . |  3 |  3  0 | 16  *  * | 1  3  0 0 | 3  3 0 | 3 1
x . . x . . |  4 |  2  2 |  * 36  * | 0  2  2 0 | 1  4 1 | 2 2
. . . x3o . |  3 |  0  3 |  *  * 16 | 0  0  3 1 | 0  3 3 | 1 3
------------+----+-------+----------+-----------+--------+----
x3o3o . . .   4 |  6  0 |  4  0  0 | 4  *  * * | 3  0 0 | 3 0
x3o . x . .   6 |  6  3 |  2  3  0 | * 24  * * | 1  2 0 | 2 1
x . . x3o .   6 |  3  6 |  0  3  2 | *  * 24 * | 0  2 1 | 1 2
. . . x3o3o   4 |  0  6 |  0  0  4 | *  *  * 4 | 0  0 3 | 0 3
------------+----+-------+----------+-----------+--------+----
x3o3o x . .   8 | 12  4 |  8  6  0 | 2  4  0 0 | 6  * * | 2 0
x3o . x3o .   9 |  9  9 |  3  9  3 | 0  3  3 0 | * 16 * | 1 1
x . . x3o3o   8 |  4 12 |  0  6  8 | 0  0  4 2 | *  * 6 | 0 2
------------+----+-------+----------+-----------+--------+----
x3o3o x3o .  12 | 18 12 | 12 18  4 | 3 12  6 0 | 3  4 0 | 4 *
x3o . x3o3o  12 | 12 18 |  4 18 12 | 0  6 12 3 | 0  4 3 | * 4

or
. . . . . .    | 16 |  6 |  6  9 | 2 18 |  6  9 | 6
---------------+----+----+-------+------+-------+--
x . . . . .  & |  2 | 48 |  2  3 | 1  9 |  4  6 | 5
---------------+----+----+-------+------+-------+--
x3o . . . .  & |  3 |  3 | 32  * | 1  3 |  3  3 | 4
x . . x . .    |  4 |  4 |  * 36 | 0  4 |  2  4 | 4
---------------+----+----+-------+------+-------+--
x3o3o . . .  &   4 |  6 |  4  0 | 8  * |  3  0 | 3
x3o . x . .  &   6 |  9 |  2  3 | * 48 |  1  2 | 3
---------------+----+----+-------+------+-------+--
x3o3o x . .  &   8 | 16 |  8  6 | 2  4 | 12  * | 2
x3o . x3o .      9 | 18 |  6  9 | 0  6 |  * 16 | 2
---------------+----+----+-------+------+-------+--
x3o3o x3o .  &  12 | 30 | 16 18 | 3 18 |  3  4 | 8

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