Acronym 4,n,m-tip
Name square - n-gon - m-gon - triprism
Circumradius sqrt[1/2+1/(4 sin2(π/n))+1/(4 sin2(π/m))]
Face vector 4nm, 12nm, 13nm+4n+4m, 6nm+8n+8m, nm+5n+5m+4, n+m+4
Especially 4,n,n-tip (m=n)   n,tes-dip (m=4)   3,3,4-tip (n=m=3)   tratess (n=3, m=4)   ax (n=m=4)   shihtip (n=m=6)  
Confer
general triprisms:
n,m,k-tip  
general polytopal classes:
Wythoffian polypeta  

Incidence matrix according to Dynkin symbol

x4o xno xmo   (n>2,m>2)

. . . . . . | 4nm |   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 | 4nm   *   * |  1   2   2  0   0  0 |  2  2  1   4  1  0  0 | 1  4 1  2  2 0 | 2 2 1
. . x . . . |   2 |   * 4nm   * |  0   2   0  1   2  0 |  1  0  2   4  0  2  1 | 1  2 0  4  2 1 | 2 1 2
. . . . x . |   2 |   *   * 4nm |  0   0   2  0   2  1 |  0  1  0   4  2  1  2 | 0  2 1  2  4 1 | 1 2 2
------------+-----+-------------+----------------------+-----------------------+----------------+------
x4o . . . . |   4 |   4   0   0 | nm   *   *  *   *  * |  2  2  0   0  0  0  0 | 1  4 1  0  0 0 | 2 2 0
x . x . . . |   4 |   2   2   0 |  * 4nm   *  *   *  * |  1  0  1   2  0  0  0 | 1  2 0  2  1 0 | 2 1 1
x . . . x . |   4 |   2   0   2 |  *   * 4nm  *   *  * |  0  1  0   2  1  0  0 | 0  2 1  1  2 0 | 1 2 1
. . xno . . |   n |   0   n   0 |  *   *   * 4m   *  * |  0  0  2   0  0  2  0 | 1  0 0  4  0 1 | 2 0 2
. . x . x . |   4 |   0   2   2 |  *   *   *  * 4nm  * |  0  0  0   2  0  1  1 | 0  1 0  2  2 1 | 1 1 2
. . . . xmo |   m |   0   0   m |  *   *   *  *   * 4n |  0  0  0   0  2  0  2 | 0  0 1  0  4 1 | 0 2 2
------------+-----+-------------+----------------------+-----------------------+----------------+------
x4o x . . .    8 |   8   4   0 |  2   4   0  0   0  0 | nm  *  *   *  *  *  * | 1  2 0  0  0 0 | 2 1 0
x4o . . x .    8 |   8   0   4 |  2   0   4  0   0  0 |  * nm  *   *  *  *  * | 0  2 1  0  0 0 | 1 2 0
x . xno . .   2n |   n  2n   0 |  0   n   0  2   0  0 |  *  * 4m   *  *  *  * | 1  0 0  2  0 0 | 2 0 1
x . x . x .    8 |   4   4   4 |  0   2   2  0   2  0 |  *  *  * 4nm  *  *  * | 0  1 0  1  1 0 | 1 1 1
x . . . xmo   2m |   m   0  2m |  0   0   m  0   0  2 |  *  *  *   * 4n  *  * | 0  0 1  0  2 0 | 0 2 1
. . xno x .   2n |   0  2n   n |  0   0   0  2   n  0 |  *  *  *   *  * 4m  * | 0  0 0  2  0 1 | 1 0 2
. . x . xmo   2m |   0   m  2m |  0   0   0  0   m  2 |  *  *  *   *  *  * 4n | 0  0 0  0  2 1 | 0 1 2
------------+-----+-------------+----------------------+-----------------------+----------------+------
x4o xno . .   4n |  4n  4n   0 |  n  4n   0  4   0  0 |  n  0  4   0  0  0  0 | m  * *  *  * * | 2 0 0
x4o x . x .   16 |  16   8   8 |  4   8   8  0   4  0 |  2  2  0   4  0  0  0 | * nm *  *  * * | 1 1 0
x4o . . xmo   4m |  4m   0  4m |  m   0  4m  0   0  4 |  0  m  0   0  4  0  0 | *  * n  *  * * | 0 2 0
x . xno x .   4n |  2n  4n  2n |  0  2n   n  4  2n  0 |  0  0  2   n  0  2  0 | *  * * 4m  * * | 1 0 1
x . x . xmo   4m |  2m  2m  4m |  0   m  2m  0  2m  4 |  0  0  0   m  2  0  2 | *  * *  * 4n * | 0 1 1
. . xno xmo   nm |   0  nm  nm |  0   0   0  m  nm  n |  0  0  0   0  0  m  n | *  * *  *  * 4 | 0 0 2
------------+-----+-------------+----------------------+-----------------------+----------------+------
x4o xno x .   8n |  8n  8n  4n | 2n  8n  4n  8  4n  0 | 2n  n  8  4n  0  4  0 | 2  n 0  4  0 0 | m * *
x4o x . xmo   8m |  8m  4m  8m | 2m  4m  8m  0  4m  8 |  m 2m  0  4m  8  0  4 | 0  m 2  0  4 0 | * n *
x . xno xmo  2nm |  nm 2nm 2nm |  0  nm  nm 2m 2nm 2n |  0  0  m  nm  n 2m 2n | 0  0 0  m  n 2 | * * 4

x x xno xmo   (n>2,m>2)

. . . . . . | 4nm |   1   1   2   2 |  1   2   2   2   2  1   4  1 |  2  2  1   4  1  1   4  1  2  2 | 1  4 1  2  2  2  2 1 | 2 2 1 1
------------+-----+-----------------+------------------------------+---------------------------------+----------------------+--------
x . . . . . |   2 | 2nm   *   *   * |  1   2   2   0   0  0   0  0 |  2  2  1   4  1  0   0  0  0  0 | 1  4 1  2  2  0  0 0 | 2 2 1 0
. x . . . . |   2 |   * 2nm   *   * |  1   0   0   2   2  0   0  0 |  2  2  0   0  0  1   4  1  0  0 | 1  4 1  0  0  2  2 0 | 2 2 0 1
. . x . . . |   2 |   *   * 4nm   * |  0   1   0   1   0  1   2  0 |  1  0  1   2  0  1   2  0  2  1 | 1  2 0  2  1  2  1 1 | 2 1 1 1
. . . . x . |   2 |   *   *   * 4nm |  0   0   1   0   1  0   2  1 |  0  1  0   2  1  0   2  1  1  2 | 0  2 1  1  2  1  2 1 | 1 2 1 1
------------+-----+-----------------+------------------------------+---------------------------------+----------------------+--------
x x . . . . |   4 |   2   2   0   0 | nm   *   *   *   *  *   *  * |  2  2  0   0  0  0   0  0  0  0 | 1  4 1  0  0  0  0 0 | 2 2 0 0
x . x . . . |   4 |   2   0   2   0 |  * 2nm   *   *   *  *   *  * |  1  0  1   2  0  0   0  0  0  0 | 1  2 0  2  1  0  0 0 | 2 1 1 0
x . . . x . |   4 |   2   0   0   2 |  *   * 2nm   *   *  *   *  * |  0  1  0   2  1  0   0  0  0  0 | 0  2 1  1  2  0  0 0 | 1 2 1 0
. x x . . . |   4 |   0   2   2   0 |  *   *   * 2nm   *  *   *  * |  1  0  0   0  0  1   2  0  0  0 | 1  2 0  0  0  2  1 0 | 2 1 0 1
. x . . x . |   4 |   0   2   0   2 |  *   *   *   * 2nm  *   *  * |  0  1  0   0  0  0   2  1  0  0 | 0  2 1  0  0  1  2 0 | 1 2 0 1
. . xno . . |   n |   0   0   n   0 |  *   *   *   *   * 4m   *  * |  0  0  1   0  0  1   0  0  2  0 | 1  0 0  2  0  2  0 1 | 2 0 1 1
. . x . x . |   4 |   0   0   2   2 |  *   *   *   *   *  * 4nm  * |  0  0  0   1  0  0   1  0  1  1 | 0  1 0  1  1  1  1 1 | 1 1 1 1
. . . . xmo |   m |   0   0   0   m |  *   *   *   *   *  *   * 4n |  0  0  0   0  1  0   0  1  0  2 | 0  0 1  0  2  0  2 1 | 0 2 1 1
------------+-----+-----------------+------------------------------+---------------------------------+----------------------+--------
x x x . . .    8 |   4   4   4   0 |  2   2   0   2   0  0   0  0 | nm  *  *   *  *  *   *  *  *  * | 1  2 0  0  0  0  0 0 | 2 1 0 0
x x . . x .    8 |   4   4   0   4 |  2   0   2   0   2  0   0  0 |  * nm  *   *  *  *   *  *  *  * | 0  2 1  0  0  0  0 0 | 1 2 0 0
x . xno . .   2n |   n   0  2n   0 |  0   n   0   0   0  2   0  0 |  *  * 2m   *  *  *   *  *  *  * | 1  0 0  2  0  0  0 0 | 2 0 1 0
x . x . x .    8 |   4   0   4   4 |  0   2   2   0   0  0   2  0 |  *  *  * 2nm  *  *   *  *  *  * | 0  1 0  1  1  0  0 0 | 1 1 1 0
x . . . xmo   2m |   m   0   0  2m |  0   0   m   0   0  0   0  2 |  *  *  *   * 2n  *   *  *  *  * | 0  0 1  0  2  0  0 0 | 0 2 1 0
. x xno . .   2n |   0   n  2n   0 |  0   0   0   n   0  2   0  0 |  *  *  *   *  * 2m   *  *  *  * | 1  0 0  0  0  2  0 0 | 2 0 0 1
. x x . x .    8 |   0   4   4   4 |  0   0   0   2   2  0   2  0 |  *  *  *   *  *  * 2nm  *  *  * | 0  1 0  0  0  1  1 0 | 1 1 0 1
. x . . xmo   2m |   0   m   0  2m |  0   0   0   0   m  0   0  2 |  *  *  *   *  *  *   * 2n  *  * | 0  0 1  0  0  0  2 0 | 0 2 0 1
. . xno x .   2n |   0   0  2n   n |  0   0   0   0   0  2   n  0 |  *  *  *   *  *  *   *  * 4m  * | 0  0 0  1  0  1  0 1 | 1 0 1 1
. . x . xmo   2m |   0   0   m  2m |  0   0   0   0   0  0   m  2 |  *  *  *   *  *  *   *  *  * 4n | 0  0 0  0  1  0  1 1 | 0 1 1 1
------------+-----+-----------------+------------------------------+---------------------------------+----------------------+--------
x x xno . .   4n |  2n  2n  4n   0 |  n  2n   0  2n   0  4   0  0 |  n  0  2   0  0  2   0  0  0  0 | m  * *  *  *  *  * * | 2 0 0 0
x x x . x .   16 |   8   8   8   8 |  4   4   4   4   4  0   4  0 |  2  2  0   2  0  0   2  0  0  0 | * nm *  *  *  *  * * | 1 1 0 0
x x . . xmo   4m |  2m  2m   0  4m |  m   0  2m   0  2m  0   0  4 |  0  m  0   0  2  0   0  2  0  0 | *  * n  *  *  *  * * | 0 2 0 0
x . xno x .   4n |  2n   0  4n  2n |  0  2n   n   0   0  4  2n  0 |  0  0  2   n  0  0   0  0  2  0 | *  * * 2m  *  *  * * | 1 0 1 0
x . x . xmo   4m |  2m   0  2m  4m |  0   m  2m   0   0  0  2m  4 |  0  0  0   m  2  0   0  0  0  2 | *  * *  * 2n  *  * * | 0 1 1 0
. x xno x .   4n |   0  2n  4n  2n |  0   0   0  2n   n  4  2n  0 |  0  0  0   0  0  2   n  0  2  0 | *  * *  *  * 2m  * * | 1 0 0 1
. x x . xmo   4m |   0  2m  2m  4m |  0   0   0   m  2m  0  2m  4 |  0  0  0   0  0  0   m  2  0  2 | *  * *  *  *  * 2n * | 0 1 0 1
. . xno xmo   nm |   0   0  nm  nm |  0   0   0   0   0  m  nm  n |  0  0  0   0  0  0   0  0  m  n | *  * *  *  *  *  * 4 | 0 0 1 1
------------+-----+-----------------+------------------------------+---------------------------------+----------------------+--------
x x xno x .   8n |  4n  4n  8n  4n | 2n  4n  2n  4n  2n  8  4n  0 | 2n  n  4  2n  0  4  2n  0  4  0 | 2  n 0  2  0  2  0 0 | m * * *
x x x . xmo   8m |  4m  4m  4m  8m | 2m  2m  4m  2m  4m  0  4m  8 |  m 2m  0  2m  4  0  2m  4  0  4 | 0  m 2  0  2  0  2 0 | * n * *
x . xno xmo  2nm |  nm   0 2nm 2nm |  0  nm  nm   0   0 2m 2nm 2n |  0  0  m  nm  n  0   0  0 2m 2n | 0  0 0  m  n  0  0 2 | * * 2 *
. x xno xmo  2nm |   0  nm 2nm 2nm |  0   0   0  nm  nm 2m 2nm 2n |  0  0  0   0  0  m  nm  n 2m 2n | 0  0 0  0  0  m  n 2 | * * * 2

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