Acronym n,m,k-tip
Name n-gon - m-gon - k-gon - triprism
Circumradius sqrt[1/(4 sin2(π/n))+1/(4 sin2(π/m))+1/(4 sin2(π/k))]
Especially n,n,k-tip (m=n)   n,n,n-tip (m=n, k=n)   n,n,4-tip (m=n, k=4)   n,tes-dip (m=4, k=4)   trittip (n=3, m=3, k=3)   3,3,4-tip   tratess (n=3, m=4, k=4)   ax (n=4, m=4, k=4)  

Incidence matrix according to Dynkin symbol

xno xmo xko   (n>2,m>2,k>2)

. . . . . . | nmk |   2   2   2 |  1   4   4  1   4  1 |  2  2  2   8  2  2  2 | 1  4 1  4  4 1 | 2 2 2
------------+-----+-------------+----------------------+-----------------------+----------------+------
x . . . . . |   2 | nmk   *   * |  1   2   2  0   0  0 |  2  2  1   4  1  0  0 | 1  4 1  2  2 0 | 2 2 1
. . x . . . |   2 |   * nmk   * |  0   2   0  1   2  0 |  1  0  2   4  0  2  1 | 1  2 0  4  2 1 | 2 1 2
. . . . x . |   2 |   *   * nmk |  0   0   2  0   2  1 |  0  1  0   4  2  1  2 | 0  2 1  2  4 1 | 1 2 2
------------+-----+-------------+----------------------+-----------------------+----------------+------
xno . . . . |   n |   n   0   0 | mk   *   *  *   *  * |  2  2  0   0  0  0  0 | 1  4 1  0  0 0 | 2 2 0
x . x . . . |   4 |   2   2   0 |  * nmk   *  *   *  * |  1  0  1   2  0  0  0 | 1  2 0  2  1 0 | 2 1 1
x . . . x . |   4 |   2   0   2 |  *   * nmk  *   *  * |  0  1  0   2  1  0  0 | 0  2 1  1  2 0 | 1 2 1
. . xmo . . |   m |   0   m   0 |  *   *   * nk   *  * |  0  0  2   0  0  2  0 | 1  0 0  4  0 1 | 2 0 2
. . x . x . |   4 |   0   2   2 |  *   *   *  * nmk  * |  0  0  0   2  0  1  1 | 0  1 0  2  2 1 | 1 1 2
. . . . xko |   k |   0   0   k |  *   *   *  *   * nm |  0  0  0   0  2  0  2 | 0  0 1  0  4 1 | 0 2 2
------------+-----+-------------+----------------------+-----------------------+----------------+------
xno x . . .   2n |  2n   n   0 |  2   n   0  0   0  0 | mk  *  *   *  *  *  * | 1  2 0  0  0 0 | 2 1 0
xno . . x .   2n |  2n   0   n |  2   0   n  0   0  0 |  * mk  *   *  *  *  * | 0  2 1  0  0 0 | 1 2 0
x . xmo . .   2m |   m  2m   0 |  0   m   0  2   0  0 |  *  * nk   *  *  *  * | 1  0 0  2  0 0 | 2 0 1
x . x . x .    8 |   4   4   4 |  0   2   2  0   2  0 |  *  *  * nmk  *  *  * | 0  1 0  1  1 0 | 1 1 1
x . . . xko   2k |   k   0  2k |  0   0   k  0   0  2 |  *  *  *   * nm  *  * | 0  0 1  0  2 0 | 0 2 1
. . xmo x .   2m |   0  2m   m |  0   0   0  2   m  0 |  *  *  *   *  * nk  * | 0  0 0  2  0 1 | 1 0 2
. . x . xko   2k |   0   k  2k |  0   0   0  0   k  2 |  *  *  *   *  *  * nm | 0  0 0  0  2 1 | 0 1 2
------------+-----+-------------+----------------------+-----------------------+----------------+------
xno xmo . .   nm |  nm  nm   0 |  m  nm   0  n   0  0 |  m  0  n   0  0  0  0 | k  * *  *  * * | 2 0 0
xno x . x .   4n |  4n  2n  2n |  4  2n  2n  0   n  0 |  2  2  0   n  0  0  0 | * mk *  *  * * | 1 1 0
xno . . xko   nk |  nk   0  nk |  k   0  nk  0   0  n |  0  k  0   0  n  0  0 | *  * m  *  * * | 0 2 0
x . xmo x .   4m |  2m  4m  2m |  0  2m   m  4  2m  0 |  0  0  2   m  0  2  0 | *  * * nk  * * | 1 0 1
x . x . xko   4k |  2k  2k  4k |  0   k  2k  0  2k  4 |  0  0  0   k  2  0  2 | *  * *  * nm * | 0 1 1
. . xmo xko   mk |   0  mk  mk |  0   0   0  k  mk  m |  0  0  0   0  0  k  m | *  * *  *  * n | 0 0 2
------------+-----+-------------+----------------------+-----------------------+----------------+------
xno xmo x .  2nm | 2nm 2nm  nm | 2m 2nm  nm 2n  nm  0 | 2m  m 2n  nm  0  n  0 | 2  m 0  n  0 0 | k * *
xno x . xko  2nk | 2nk  nk 2nk | 2k  nk 2nk  0  nk 2n |  k 2k  0  nk 2n  0  n | 0  k 2  0  n 0 | * m *
x . xmo xko  2mk |  mk 2mk 2mk |  0  mk  mk 2k 2mk 2m |  0  0  k  mk  m 2k 2m | 0  0 0  k  m 2 | * * n

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