Acronym n,tic-dip
Name n-gon - truncated-cube duoprism
Circumradius sqrt[sqrt(2)+7/4+1/(4 sin2(π/n))]
Especially tratic (n=3)   squatic (n=4)   hatic (n=6)   otic (n=8)  
Confer
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

xno o3x4x   (n>2)

. . . . . | 24n |   2   2   1 |  1   4   2  1  2 |  2  1  2  4 1 | 1 2 2
----------+-----+-------------+------------------+---------------+------
x . . . . |   2 | 24n   *   * |  1   2   1  0  0 |  2  1  1  2 0 | 1 2 1
. . . x . |   2 |   * 24n   * |  0   2   0  1  1 |  1  0  2  2 1 | 1 1 2
. . . . x |   2 |   *   * 12n |  0   0   2  0  2 |  0  1  0  4 1 | 0 2 2
----------+-----+-------------+------------------+---------------+------
xno . . . |   n |   n   0   0 | 24   *   *  *  * |  2  1  0  0 0 | 1 2 0
x . . x . |   4 |   2   2   0 |  * 24n   *  *  * |  1  0  1  1 0 | 1 1 1
x . . . x |   4 |   2   0   2 |  *   * 12n  *  * |  0  1  0  2 0 | 0 2 1
. . o3x . |   3 |   0   3   0 |  *   *   * 8n  * |  0  0  2  0 1 | 1 0 2
. . . x4x |   8 |   0   4   4 |  *   *   *  * 6n |  0  0  0  2 1 | 0 1 2
----------+-----+-------------+------------------+---------------+------
xno . x .   2n |  2n   n   0 |  2   n   0  0  0 | 24  *  *  * * | 1 1 0
xno . . x   2n |  2n   0   n |  2   0   n  0  0 |  * 12  *  * * | 0 2 0
x . o3x .    6 |   3   6   0 |  0   3   0  2  0 |  *  * 8n  * * | 1 0 1
x . . x4x   16 |   8   8   8 |  0   4   4  0  2 |  *  *  * 6n * | 0 1 1
. . o3x4x   24 |   0  24  12 |  0   0   0  8  6 |  *  *  *  * n | 0 0 2
----------+-----+-------------+------------------+---------------+------
xno o3x .   3n |  3n  3n   0 |  3  3n   0  n  0 |  3  0  n  0 0 | 8 * *
xno . x4x   8n |  8n  4n  4n |  8  4n  4n  0  n |  4  4  0  n 0 | * 6 *
x . o3x4x   48 |  24  48  24 |  0  24  12 16 12 |  0  0  8  6 2 | * * n

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