Acronym	2n-p
TOCID symbol	(2n)P, t(n)P
Name	2n-gonal prism
Circumradius	sqrt[1/4+1/(4 sin2(π/2n))]
Vertex figure	[42,2n]
Snub derivation / VRML	⭳   ⭳   ⭳
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Face vector	4n, 6n, 2n+2
Especially	cube (n=2)   hip (n=3)   op (n=4)   dip (n=5)   twip (n=6)   azip (n=∞)
Confer	more general: 2n/d-p   Grünbaumian relatives: 2n/2-p   general polytopal classes: Wythoffian polyhedra
External links

Although in here n>1 is allowed, snubbing links require n>2 generally. Nonetheless, s2s4o well is possible too (it even becomes a regular polyhedron), it just has a different incidence structure because of degeneracies.

Incidence matrix according to Dynkin symbol

x x2no   (n>1)

. .  . | 4n |  1  2 |  2 1
-------+----+-------+-----
x .  . |  2 | 2n  * |  2 0
. x  . |  2 |  * 4n |  1 1
-------+----+-------+-----
x x  . |  4 |  2  2 | 2n *
. x2no | 2n |  0 2n |  * 2

snubbed forms: x2s2no (for n>2), x2s2no (for even n>2), s2s2no (for n>2)

x xnx   (n>1)

. . . | 4n |  1  1  1 | 1 1 1
------+----+----------+------
x . . |  2 | 2n  *  * | 1 1 0
. x . |  2 |  * 2n  * | 1 0 1
. . x |  2 |  *  * 2n | 0 1 1
------+----+----------+------
x x . |  4 |  2  2  0 | n * *
x . x |  4 |  2  0  2 | * n *
. xnx | 2n |  0  n  n | * * 2

snubbed forms: x2βnx (for n>2), x2snx (for even n>2), β2βnx (for n>2), s2snx (for even n>2), x2sns (for n>2), x2sns (for even n>2), s2sns (for n>2)

s2s2nx   (n>1)

demi( . .  . ) | 4n |  1  1  1 | 1  2
---------------+----+----------+-----
      s2s      |  2 | 2n  *  * | 0  2
demi( . .  x ) |  2 |  * 2n  * | 1  1
sefa( . s2nx ) |  2 |  *  * 2n | 1  1
---------------+----+----------+-----
        s2nx   ♦ 2n |  0  n  n | 2  *
sefa( s2s2nx ) |  4 |  2  1  1 | * 2n

starting figure: x x2nx

x2s2nx   (n>1)

demi( . .  . ) | 4n |  1  1  1 | 1 1 1
---------------+----+----------+------
demi( x .  . ) |  2 | 2n  *  * | 0 1 1
demi( . .  x ) |  2 |  * 2n  * | 1 1 0
sefa( . s2nx ) |  2 |  *  * 2n | 1 0 1
---------------+----+----------+------
      . s2nx   ♦ 2n |  0  n  n | 2 * *
demi( x .  x ) |  4 |  2  2  0 | * n *
sefa( x2s2nx ) |  4 |  2  0  2 | * * n

starting figure: x x2nx

x2s2ns   (n>1)

demi( . .  . ) | 4n |  1  2 | 1  2
---------------+----+-------+-----
demi( x .  . ) |  2 | 2n  * | 0  2
sefa( . s2ns ) |  2 |  * 4n | 1  1
---------------+----+-------+-----
      . s2ns   ♦ 2n |  0 2n | 2  *
sefa( x2s2ns ) |  4 |  2  2 | * 2n

starting figure: x x2nx

x2s4no   (n>1)

demi( . .  . ) | 4n |  1  2 | 1  2
---------------+----+-------+-----
demi( x .  . ) |  2 | 2n  * | 0  2
sefa( . s4no ) |  2 |  * 4n | 1  1
---------------+----+-------+-----
      . s4no   ♦ 2n |  0 2n | 2  *
sefa( x2s4no ) |  4 |  2  2 | * 2n

starting figure: x x4no

xx2noo&#x   (n>1)   → height = 1
({2n} || {2n})

o.2no.    | 2n  * |  2  1  0 | 1  2 0
.o2n.o    |  * 2n |  0  1  2 | 0  2 1
----------+-------+----------+-------
x.  ..    |  2  0 | 2n  *  * | 1  1 0
oo2noo&#x |  1  1 |  * 2n  * | 0  2 0
.x  ..    |  0  2 |  *  * 2n | 0  1 1
----------+-------+----------+-------
x.2no.    | 2n  0 | 2n  0  0 | 1  * *
xx  ..&#x |  2  2 |  1  2  1 | * 2n *
.x2n.o    |  0 2n |  0  0 2n | *  * 1

xxnxx&#x   (n>1)   → height = 1
({2n} || {2n})

o.no.    | 2n  * | 1 1  1 0 0 | 1 1 1 0
.on.o    |  * 2n | 0 0  1 1 1 | 0 1 1 1
---------+-------+------------+--------
x. ..    |  2  0 | n *  * * * | 1 1 0 0
.. x.    |  2  0 | * n  * * * | 1 0 1 0
oonoo&#x |  1  1 | * * 2n * * | 0 1 1 0
.x ..    |  0  2 | * *  * n * | 0 1 0 1
.. .x    |  0  2 | * *  * * n | 0 0 1 1
---------+-------+------------+--------
x.nx.    | 2n  0 | n n  0 0 0 | 1 * * *
xx ..&#x |  2  2 | 1 0  2 1 0 | * n * *
.. xx&#x |  2  2 | 0 1  2 0 1 | * * n *
.xn.x    |  0 2n | 0 0  0 n n | * * * 1