Acronym n,ike-dip
Name n-gon - icosahedron duoprism
Circumradius sqrt[(5+sqrt(5))/8+1/(4 sin2(π/n))]
Especially trike (n=3)   squike (n=4)   pike (n=5)   hike (n=6)   oike (n=8)  

Incidence matrix according to Dynkin symbol

xno x3o5o   (n>2)

. . . . . | 12n |   2   5 |  1  10   5 |  5  10 1 |  5 2
----------+-----+---------+------------+----------+-----
x . . . . |   2 | 12n   * |  1   5   0 |  5   5 0 |  5 1
. . x . . |   2 |   * 30n |  0   2   2 |  1   4 1 |  2 2
----------+-----+---------+------------+----------+-----
xno . . . |   n |   n   0 | 12   *   * |  5   0 0 |  5 0
x . x . . |   4 |   2   2 |  * 30n   * |  1   2 0 |  2 1
. . x3o . |   3 |   0   3 |  *   * 20n |  0   2 1 |  1 2
----------+-----+---------+------------+----------+-----
xno x . .   2n |  2n   n |  2   n   0 | 30   * * |  2 0
x . x3o .    6 |   3   6 |  0   3   2 |  * 20n * |  1 1
. . x3o5o   12 |   0  30 |  0   0  20 |  *   * n |  0 2
----------+-----+---------+------------+----------+-----
xno x3o .   3n |  3n  3n |  3  3n   n |  3   n 0 | 20 *
x . x3o5o   24 |  12  60 |  0  30  40 |  0  20 2 |  * n

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