Acronym n,tid-dip
Name n-gon - truncated-dodecahedron duoprism
Circumradius sqrt[(37+15 sqrt(5))/8+1/(4 sin2(π/n))]
Especially tratid (n=3)   squatid (n=4)   hatid (n=6)   otid (n=8)  

Incidence matrix according to Dynkin symbol

xno o3x5x   (n>2)

. . . . . | 60n |   2   2   1 |  1   4   2   1   2 |  2  1   2   4 1 |  1  2 2
----------+-----+-------------+--------------------+-----------------+--------
x . . . . |   2 | 60n   *   * |  1   2   1   0   0 |  2  1   1   2 0 |  1  2 1
. . . x . |   2 |   * 60n   * |  0   2   0   1   1 |  1  0   2   2 1 |  1  1 2
. . . . x |   2 |   *   * 30n |  0   0   2   0   2 |  0  1   0   4 1 |  0  2 2
----------+-----+-------------+--------------------+-----------------+--------
xno . . . |   n |   n   0   0 | 60   *   *   *   * |  2  1   0   0 0 |  1  2 0
x . . x . |   4 |   2   2   0 |  * 60n   *   *   * |  1  0   1   1 0 |  1  1 1
x . . . x |   4 |   2   0   2 |  *   * 30n   *   * |  0  1   0   2 0 |  0  2 1
. . o3x . |   3 |   0   3   0 |  *   *   * 20n   * |  0  0   2   0 1 |  1  0 2
. . . x5x |  10 |   0   5   5 |  *   *   *   * 12n |  0  0   0   2 1 |  0  1 2
----------+-----+-------------+--------------------+-----------------+--------
xno . x .   2n |  2n   n   0 |  2   n   0   0   0 | 60  *   *   * * |  1  1 0
xno . . x   2n |  2n   0   n |  2   0   n   0   0 |  * 30   *   * * |  0  2 0
x . o3x .    6 |   3   6   0 |  0   3   0   2   0 |  *  * 20n   * * |  1  0 1
x . . x5x   20 |  10  10  10 |  0   5   5   0   2 |  *  *   * 12n * |  0  1 1
. . o3x5x   60 |   0  60  30 |  0   0   0  20  12 |  *  *   *   * n |  0  0 2
----------+-----+-------------+--------------------+-----------------+--------
xno o3x .   3n |  3n  3n   0 |  3  3n   0   n   0 |  3  0   n   0 0 | 20  * *
xno . x5x  10n | 10n  5n  5n | 10  5n  5n   0   n |  5  5   0   n 0 |  * 12 *
x . o3x5x  120 |  60 120  60 |  0  60  30  40  24 |  0  0  20  12 2 |  *  * n

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