Acronym n,n,n-tip
Name n-gon - n-gon - n-gon - triprism
Circumradius sqrt[3/(4 sin2(π/n))]
Especially trittip (n=3)   ax (n=4)   pettip (n=5)   hittip (n=6)   hettip (n=7)   otip (n=8)   etip (n=9)   dittip (n=10)  
Confer
general triprisms:
n,m,k-tip   n,n,m-tip  

Incidence matrix according to Dynkin symbol

xno xno xno   (n>2)

. . . . . . | nnn |   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 | nnn   *   * |  1   2   2  0   0  0 |  2  2  1   4  1  0  0 | 1  4 1  2  2 0 | 2 2 1
. . x . . . |   2 |   * nnn   * |  0   2   0  1   2  0 |  1  0  2   4  0  2  1 | 1  2 0  4  2 1 | 2 1 2
. . . . x . |   2 |   *   * nnn |  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 | nn   *   *  *   *  * |  2  2  0   0  0  0  0 | 1  4 1  0  0 0 | 2 2 0
x . x . . . |   4 |   2   2   0 |  * nnn   *  *   *  * |  1  0  1   2  0  0  0 | 1  2 0  2  1 0 | 2 1 1
x . . . x . |   4 |   2   0   2 |  *   * nnn  *   *  * |  0  1  0   2  1  0  0 | 0  2 1  1  2 0 | 1 2 1
. . xno . . |   n |   0   n   0 |  *   *   * nn   *  * |  0  0  2   0  0  2  0 | 1  0 0  4  0 1 | 2 0 2
. . x . x . |   4 |   0   2   2 |  *   *   *  * nnn  * |  0  0  0   2  0  1  1 | 0  1 0  2  2 1 | 1 1 2
. . . . xno |   n |   0   0   n |  *   *   *  *   * nn |  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 | nn  *  *   *  *  *  * | 1  2 0  0  0 0 | 2 1 0
xno . . x .   2n |  2n   0   n |  2   0   n  0   0  0 |  * nn  *   *  *  *  * | 0  2 1  0  0 0 | 1 2 0
x . xno . .   2n |   n  2n   0 |  0   n   0  2   0  0 |  *  * nn   *  *  *  * | 1  0 0  2  0 0 | 2 0 1
x . x . x .    8 |   4   4   4 |  0   2   2  0   2  0 |  *  *  * nnn  *  *  * | 0  1 0  1  1 0 | 1 1 1
x . . . xno   2n |   n   0  2n |  0   0   n  0   0  2 |  *  *  *   * nn  *  * | 0  0 1  0  2 0 | 0 2 1
. . xno x .   2n |   0  2n   n |  0   0   0  2   n  0 |  *  *  *   *  * nn  * | 0  0 0  2  0 1 | 1 0 2
. . x . xno   2n |   0   n  2n |  0   0   0  0   n  2 |  *  *  *   *  *  * nn | 0  0 0  0  2 1 | 0 1 2
------------+-----+-------------+----------------------+-----------------------+----------------+------
xno xno . .   nn |  nn  nn   0 |  n  nn   0  n   0  0 |  n  0  n   0  0  0  0 | n  * *  *  * * | 2 0 0
xno x . x .   4n |  4n  2n  2n |  4  2n  2n  0   n  0 |  2  2  0   n  0  0  0 | * nn *  *  * * | 1 1 0
xno . . xno   nn |  nn   0  nn |  n   0  nn  0   0  n |  0  n  0   0  n  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 | *  * * nn  * * | 1 0 1
x . x . xno   4n |  2n  2n  4n |  0   n  2n  0  2n  4 |  0  0  0   n  2  0  2 | *  * *  * nn * | 0 1 1
. . xno xno   nn |   0  nn  nn |  0   0   0  n  nn  n |  0  0  0   0  0  n  n | *  * *  *  * n | 0 0 2
------------+-----+-------------+----------------------+-----------------------+----------------+------
xno xno x .  2nn | 2nn 2nn  nn | 2n 2nn  nn 2n  nn  0 | 2n  n 2n  nn  0  n  0 | 2  n 0  n  0 0 | n * *
xno x . xno  2nn | 2nn  nn 2nn | 2n  nn 2nn  0  nn 2n |  n 2n  0  nn 2n  0  n | 0  n 2  0  n 0 | * n *
x . xno xno  2nn |  nn 2nn 2nn |  0  nn  nn 2n 2nn 2n |  0  0  n  nn  n 2n 2n | 0  0 0  n  n 2 | * * n
or
. . . . . .    | nnn |    3 |   3  12 |  12   8 |  3  12 |  6
---------------+-----+------+---------+---------+--------+---
x . . . . .  & |   2 | 3nnn |   1   4 |   6   4 |  2   8 |  5
---------------+-----+------+---------+---------+--------+---
xno . . . .  & |   n |    n | 3nn   * |   4   0 |  2   4 |  4
x . x . . .  & |   4 |    4 |   * 3nn |   2   2 |  1   5 |  4
---------------+-----+------+---------+---------+--------+---
xno x . . .  &   2n |   3n |   2   n | 6nn   * |  1   2 |  3
x . x . x .       8 |   12 |   0   6 |   * nnn |  0   3 |  3
---------------+-----+------+---------+---------+--------+---
xno xno . .  &   nn |  2nn |  2n  nn |  2n   0 | 3n   * |  2
xno x . x .  &   4n |   8n |   4  5n |   4   n |  * 3nn |  2
---------------+-----+------+---------+---------+--------+---
xno xno x .  &  2nn |  5nn |  4n 4nn |  6n  nn |  2  2n | 3n

© 2004-2021
top of page