Acronym (n,m-ap)-dip
Name n-gon - m-antiprism - duoprism
Circumradius sqrt[1/(4 sin2(π/n))+(3-2 cos(π/m))/(8-8 cos(π/m))]
Face vector 2nm, 6nm, 6nm+2n+2m, 2nm+3n+4m, n+2m+2
Especially n,oct-dip (m=3)  
troct (n=3,m=3)   squoct (n=4,m=3)   poct (n=5,m=3)   stoct (n=5/2,m=3)   hoct (n=6,m=3)   owoct (n=8,m=3)   stowoct (n=8/3,m=3)  
Confer
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

xx-n-oo xo-m-ox&#x   → height = sqrt[(1+2 cos(π/m))/(2+2 cos(π/m))]
(n,m-dip || para-gyro n,m-dip)

o.-n-o. o.-m-o.    & | 2nm |   2   2   2 |  1   4  1   4   3 |  2  2  2   6 1 | 1  3 2
---------------------+-----+-------------+-------------------+----------------+-------
x.   .. ..   ..    & |   2 | 2nm   *   * |  1   2  0   2   0 |  2  1  2   3 0 | 1  3 1
..   .. x.   ..    & |   2 |   * 2nm   * |  0   2  1   0   1 |  1  2  0   2 1 | 1  1 2
oo-n-oo oo-m-oo&#x   |   2 |   *   * 2nm |  0   0  0   2   2 |  0  0  1   4 1 | 0  2 2
---------------------+-----+-------------+-------------------+----------------+-------
x.-n-o. ..   ..    & |   n |   n   0   0 | 2m   *  *   *   * |  2  0  2   0 0 | 1  3 0
x.   .. x.   ..    & |   4 |   2   2   0 |  * 2nm  *   *   * |  1  1  0   1 0 | 1  1 1
..   .. x.-m-o.    & |   m |   0   m   0 |  *   * 2n   *   * |  0  2  0   0 1 | 1  0 2
xx   .. ..   ..&#x   |   4 |   2   0   2 |  *   *  * 2nm   * |  0  0  1   2 0 | 0  2 1
..   .. xo   ..&#x & |   3 |   0   1   2 |  *   *  *   * 2nm |  0  0  0   2 1 | 0  1 2
---------------------+-----+-------------+-------------------+----------------+-------
x.-n-o. x.   ..    &   2n |  2n   n   0 |  2   n  0   0   0 | 2m  *  *   * * | 1  1 0
x.   .. x.-m-o.    &   2m |   m  2m   0 |  0   m  2   0   0 |  * 2n  *   * * | 1  0 1
xx-n-oo ..   ..&#x     2n |  2n   0   n |  2   0  0   n   0 |  *  * 2m   * * | 0  2 0
xx   .. xo   ..&#x &    6 |   3   2   4 |  0   1  0   2   2 |  *  *  * 2nm * | 0  1 1
..   .. xo-m-ox&#x     2m |   0  2m  2m |  0   0  2   0  2m |  *  *  *   * n | 0  0 2
---------------------+-----+-------------+-------------------+----------------+-------
x.-n-o. x.-m-o.    &   nm |  nm  nm   0 |  m  nm  n   0   0 |  m  n  0   0 0 | 2  * *
xx-n-oo xo   ..&#x &   3n |  3n   n  2n |  3   n  0  2n   n |  1  0  2   n 0 | * 2m *
xx   .. xo-m-ox&#x     4m |  2m  4m  4m |  0  2m  4  2m  4m |  0  2  0  2m 2 | *  * n

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