4,n,n-tip

Acronym	4,n,n-tip
Name	square - n-gon - n-gon - triprism
Circumradius	sqrt[1/2+1/(2 sin²(π/n))]
Face vector	4n², 12n², 13n²+8n, 6n²+16n, n²+10n+4, 2n+4
Especially	3,3,4-tip (n=3) ax (n=4) shihtip (n=6)
Confer	general triprisms: n,m,k-tip n,n,m-tip general polytopal classes: Wythoffian polypeta

Incidence matrix according to Dynkin symbol

xno xno x4o   (n>2)

. . . . . . | 4nn |   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 | 4nn   *   * |  1   2   2  0   0  0 |  2  2  1   4  1  0  0 | 1  4 1  2  2 0 | 2 2 1
. . x . . . |   2 |   * 4nn   * |  0   2   0  1   2  0 |  1  0  2   4  0  2  1 | 1  2 0  4  2 1 | 2 1 2
. . . . x . |   2 |   *   * 4nn |  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 | 4n   *   *  *   *  * |  2  2  0   0  0  0  0 | 1  4 1  0  0 0 | 2 2 0
x . x . . . |   4 |   2   2   0 |  * 4nn   *  *   *  * |  1  0  1   2  0  0  0 | 1  2 0  2  1 0 | 2 1 1
x . . . x . |   4 |   2   0   2 |  *   * 4nn  *   *  * |  0  1  0   2  1  0  0 | 0  2 1  1  2 0 | 1 2 1
. . xno . . |   n |   0   n   0 |  *   *   * 4n   *  * |  0  0  2   0  0  2  0 | 1  0 0  4  0 1 | 2 0 2
. . x . x . |   4 |   0   2   2 |  *   *   *  * 4nn  * |  0  0  0   2  0  1  1 | 0  1 0  2  2 1 | 1 1 2
. . . . x4o |   4 |   0   0   4 |  *   *   *  *   * 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 | 4n  *  *   *  *  *  * | 1  2 0  0  0 0 | 2 1 0
xno . . x . ♦  2n |  2n   0   n |  2   0   n  0   0  0 |  * 4n  *   *  *  *  * | 0  2 1  0  0 0 | 1 2 0
x . xno . . ♦  2n |   n  2n   0 |  0   n   0  2   0  0 |  *  * 4n   *  *  *  * | 1  0 0  2  0 0 | 2 0 1
x . x . x . ♦   8 |   4   4   4 |  0   2   2  0   2  0 |  *  *  * 4nn  *  *  * | 0  1 0  1  1 0 | 1 1 1
x . . . x4o ♦   8 |   4   0   8 |  0   0   4  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 |  *  *  *   *  * 4n  * | 0  0 0  2  0 1 | 1 0 2
. . x . x4o ♦   8 |   0   4   8 |  0   0   0  0   4  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 | 4  * *  *  * * | 2 0 0
xno x . x . ♦  4n |  4n  2n  2n |  4  2n  2n  0   n  0 |  2  2  0   n  0  0  0 | * 4n *  *  * * | 1 1 0
xno . . x4o ♦  4n |  4n   0  4n |  4   0  4n  0   0  n |  0  4  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 | *  * * 4n  * * | 1 0 1
x . x . x4o ♦  16 |   8   8  16 |  0   4   8  0   8  4 |  0  0  0   4  2  0  2 | *  * *  * nn * | 0 1 1
. . xno x4o ♦  4n |   0  4n  4n |  0   0   0  4  4n  n |  0  0  0   0  0  4  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 | 4 * *
xno x . x4o ♦  8n |  8n  4n  8n |  8  4n  8n  0  4n 2n |  4  8  0  4n 2n  0  n | 0  4 2  0  n 0 | * n *
x . xno x4o ♦  8n |  4n  8n  8n |  0  4n  4n  8  8n 2n |  0  0  4  4n  n  8 2n | 0  0 0  4  n 2 | * * n

or
. . . . . .    | 4nn |   4   2 |  2   4   8  1 |  4  4   8   4 | 1  8  2  4 | 2  4
---------------+-----+---------+---------------+---------------+------------+-----
x . . . . .  & |   2 | 8nn   * |  1   2   2  0 |  3  2   4   1 | 1  6  1  2 | 2  3
. . . . x .    |   2 |   * 4nn |  0   0   4  1 |  0  2   4   4 | 0  4  2  4 | 1  4
---------------+-----+---------+---------------+---------------+------------+-----
xno . . . .  & |   n |   n   0 | 8n   *   *  * |  2  2   0   0 | 1  4  1  0 | 2  2
x . x . . .    |   4 |   4   0 |  * 4nn   *  * |  2  0   2   0 | 1  4  0  1 | 2  2
x . . . x .  & |   4 |   2   2 |  *   * 8nn  * |  0  1   2   1 | 0  3  1  2 | 1  3
. . . . x4o    |   4 |   0   4 |  *   *   * nn |  0  0   0   4 | 0  0  2  4 | 0  4
---------------+-----+---------+---------------+---------------+------------+-----
xno x . . .  & ♦  2n |  3n   0 |  2   n   0  0 | 8n  *   *   * | 1  2  0  0 | 2  1
xno . . x .  & ♦  2n |  2n   n |  2   0   n  0 |  * 8n   *   * | 0  2  1  0 | 1  2
x . x . x .    ♦   8 |   8   4 |  0   2   4  0 |  *  * 4nn   * | 0  2  0  1 | 1  2
x . . . x4o  & ♦   8 |   4   8 |  0   0   4  2 |  *  *   * 2nn | 0  0  1  2 | 0  3
---------------+-----+---------+---------------+---------------+------------+-----
xno xno . .    ♦  nn | 2nn   0 | 2n  nn   0  0 | 2n  0   0   0 | 4  *  *  * | 2  0
xno x . x .  & ♦  4n |  6n  2n |  4  2n  3n  0 |  2  2   n   0 | * 8n  *  * | 1  1
xno . . x4o  & ♦  4n |  4n  4n |  4   0  4n  n |  0  4   0   n | *  * 2n  * | 0  2
x . x . x4o    ♦  16 |  16  16 |  0   4  16  4 |  0  0   4   4 | *  *  * nn | 0  2
---------------+-----+---------+---------------+---------------+------------+-----
xno xno x .    ♦ 2nn | 4nn  nn | 4n 2nn 2nn  0 | 4n 2n  nn   0 | 2 2n  0  0 | 4  *
xno x . x4o  & ♦  8n |  8n  8n |  8  4n 12n 2n |  4  8  4n  3n | 0  4  2  n | * 2n

x x xno xno   (n>2)

. . . . . . | 4nn |   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 | 2nn   *   *   * |  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 |   * 2nn   *   * |  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 |   *   * 4nn   * |  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 |   *   *   * 4nn |  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 | nn   *   *   *   *  *   *  * |  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 |  * 2nn   *   *   *  *   *  * |  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 |  *   * 2nn   *   *  *   *  * |  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 |  *   *   * 2nn   *  *   *  * |  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 |  *   *   *   * 2nn  *   *  * |  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 |  *   *   *   *   * 4n   *  * |  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 |  *   *   *   *   *  * 4nn  * |  0  0  0   1  0  0   1  0  1  1 | 0  1 0  1  1  1  1 1 | 1 1 1 1
. . . . xno |   n |   0   0   0   n |  *   *   *   *   *  *   * 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 | nn  *  *   *  *  *   *  *  *  * | 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 |  * nn  *   *  *  *   *  *  *  * | 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 |  *  * 2n   *  *  *   *  *  *  * | 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 |  *  *  * 2nn  *  *   *  *  *  * | 0  1 0  1  1  0  0 0 | 1 1 1 0
x . . . xno ♦  2n |   n   0   0  2n |  0   0   n   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 |  *  *  *   *  * 2n   *  *  *  * | 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 |  *  *  *   *  *  * 2nn  *  *  * | 0  1 0  0  0  1  1 0 | 1 1 0 1
. x . . xno ♦  2n |   0   n   0  2n |  0   0   0   0   n  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 |  *  *  *   *  *  *   *  * 4n  * | 0  0 0  1  0  1  0 1 | 1 0 1 1
. . x . xno ♦  2n |   0   0   n  2n |  0   0   0   0   0  0   n  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 | n  * *  *  *  *  * * | 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 | * nn *  *  *  *  * * | 1 1 0 0
x x . . xno ♦  4n |  2n  2n   0  4n |  n   0  2n   0  2n  0   0  4 |  0  n  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 | *  * * 2n  *  *  * * | 1 0 1 0
x . x . xno ♦  4n |  2n   0  2n  4n |  0   n  2n   0   0  0  2n  4 |  0  0  0   n  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 | *  * *  *  * 2n  * * | 1 0 0 1
. x x . xno ♦  4n |   0  2n  2n  4n |  0   0   0   n  2n  0  2n  4 |  0  0  0   0  0  0   n  2  0  2 | *  * *  *  *  * 2n * | 0 1 0 1
. . xno xno ♦  nn |   0   0  nn  nn |  0   0   0   0   0  n  nn  n |  0  0  0   0  0  0   0  0  n  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 | n * * *
x x x . xno ♦  8n |  4n  4n  4n  8n | 2n  2n  4n  2n  4n  0  4n  8 |  n 2n  0  2n  4  0  2n  4  0  4 | 0  n 2  0  2  0  2 0 | * n * *
x . xno xno ♦ 2nn |  nn   0 2nn 2nn |  0  nn  nn   0   0 2n 2nn 2n |  0  0  n  nn  n  0   0  0 2n 2n | 0  0 0  n  n  0  0 2 | * * 2 *
. x xno xno ♦ 2nn |   0  nn 2nn 2nn |  0   0   0  nn  nn 2n 2nn 2n |  0  0  0   0  0  n  nn  n 2n 2n | 0  0 0  0  0  n  n 2 | * * * 2

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