Acronym	4,n-dip, K-4.177
Name	square - n-gonal duoprism
Circumradius	sqrt[1/2+1/(4 sin2(π/n))]
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Face vector	4n, 8n, 5n+4, n+4
Especially	4,2m-dip (n even)   cube (n=2)*   tisdip (n=3)   tes (n=4)   squipdip (n=5)   shiddip (n=6)   sodip (n=8)   squadedip (n=10)   sitwadip (n=12)
Confer	general duoprisms: n,m-dip   general polytopal classes: Wythoffian polychora   segmentochora
External links

* The case n=2 (cube) would belong here as well by concept. So it would have a different incidence matrix, because of the degeneracy of the n-gon. It even has a different dimensionality as a global figure.

Incidence matrix according to Dynkin symbol

x4o xno   (n>2)

. . . . | 4n |  2  2 | 1  4 1 | 2 2
--------+----+-------+--------+----
x . . . |  2 | 4n  * | 1  2 0 | 2 1
. . x . |  2 |  * 4n | 0  2 1 | 1 2
--------+----+-------+--------+----
x4o . . |  4 |  4  0 | n  * * | 2 0
x . x . |  4 |  2  2 | * 4n * | 1 1
. . xno |  n |  0  n | *  * 4 | 0 2
--------+----+-------+--------+----
x4o x . ♦  8 |  8  4 | 2  4 0 | n *
x . xno ♦ 2n |  n 2n | 0  n 2 | * 4

x x xno   (n>2)

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

x x sns   (n>2)

. . demi( . . ) | 4n |  1  1  2 | 1  2  2 1 | 2 1 1
----------------+----+----------+-----------+------
x . demi( . . ) |  2 | 2n  *  * | 1  2  0 0 | 2 1 0
. x demi( . . ) |  2 |  * 2n  * | 1  0  2 0 | 2 0 1
. . sefa( sns ) |  2 |  *  * 4n | 0  1  1 1 | 1 1 1
----------------+----+----------+-----------+------
x x demi( . . ) |  4 |  2  2  0 | n  *  * * | 2 0 0
x . sefa( sns ) |  4 |  2  0  2 | * 2n  * * | 1 1 0
. x sefa( sns ) |  4 |  0  2  2 | *  * 2n * | 1 0 1
. .       sns   ♦  n |  0  0  n | *  *  * 4 | 0 1 1
----------------+----+----------+-----------+------
x x sefa( sns ) ♦  8 |  4  4  4 | 2  2  2 0 | n * *
x .       sns   ♦ 2n |  n  0 2n | 0  n  0 2 | * 2 *
. x       sns   ♦ 2n |  0  n 2n | 0  0  n 2 | * * 2

xx xxnoo&#x   (n>2)   → height = 1
({n}-p || {n}-p)

o. o. o.    | 2n  * | 1  2  1 0  0 | 2 1 1  2 0 0 | 1 2 1 0
.o .o .o    |  * 2n | 0  0  1 1  2 | 0 0 1  2 2 1 | 0 2 1 1
------------+-------+--------------+--------------+--------
x. .. ..    |  2  0 | n  *  * *  * | 2 0 1  0 0 0 | 1 2 0 0
.. x. ..    |  2  0 | * 2n  * *  * | 1 1 0  1 0 0 | 1 1 1 0
oo oonoo&#x |  1  1 | *  * 2n *  * | 0 0 1  2 0 0 | 0 2 1 0
.x .. ..    |  0  2 | *  *  * n  * | 0 0 1  0 2 0 | 0 2 0 1
.. .x ..    |  0  2 | *  *  * * 2n | 0 0 0  1 1 1 | 0 1 1 1
------------+-------+--------------+--------------+--------
x. x. ..    |  4  0 | 2  2  0 0  0 | n * *  * * * | 1 1 0 0
.. x.no.    |  n  0 | 0  n  0 0  0 | * 2 *  * * * | 1 0 1 0
xx .. ..&#x |  2  2 | 1  0  2 1  0 | * * n  * * * | 0 2 0 0
.. xx ..&#x |  2  2 | 0  1  2 0  1 | * * * 2n * * | 0 1 1 0
.x .x ..    |  0  4 | 0  0  0 2  2 | * * *  * n * | 0 1 0 1
.. .xn.o    |  0  n | 0  0  0 0  n | * * *  * * 2 | 0 0 1 1
------------+-------+--------------+--------------+--------
x. x.no.    ♦ 2n  0 | n 2n  0 0  0 | n 2 0  0 0 0 | 1 * * *
xx xx ..&#x ♦  4  4 | 2  2  4 2  2 | 1 0 2  2 1 0 | * n * *
.. xxnoo&#x ♦  n  n | 0  n  n 0  n | 0 1 0  n 0 1 | * * 2 *
.x .xn.o    ♦  0 2n | 0  0  0 n 2n | 0 0 0  0 n 2 | * * * 1