Acronym	azip
TOCID symbol	(∞)P
Name	apeirogonal prism
	©
Vertex figure	[42,∞]
Confer	general polytopal classes: n-p   2n-p   tiling
External links

Although this looks just like a mere stripe of squares, it still is a tiling of the complete plane: both seemingly empty half-planes may be considered filled by an inifinite-gon each.

It also is an extension of the general n-gonal prism, thereby becoming a flat tiling.

Incidence matrix according to Dynkin symbol

x xNo   (N → ∞)

. . . | 2N | 1  2 | 2 1
------+----+------+----
x . . |  2 | N  * | 2 0
. x . |  2 | * 2N | 1 1
------+----+------+----
x x . |  4 | 2  2 | N *
. xNo ♦  N | 0  N | * 2

snubbed forms: s2sNo (N even)

x xNx   (N → ∞)

. . . | 4N |  1  1  1 | 1 1 1
------+----+----------+------
x . . |  2 | 2N  *  * | 1 1 0
. x . |  2 |  *  6  * | 1 0 1
. . x |  2 |  *  *  6 | 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: s2sNs

xxNoo&#x     (N → ∞)   → height = 1
({N} || {N})

o.No.    | N * | 2 1 0 | 1 2 0
.oN.o    | * N | 0 1 2 | 0 2 1
---------+-----+-------+------
x. ..    | 2 0 | N * * | 1 1 0
ooNoo&#x | 1 1 | * N * | 0 2 0
.x ..    | 0 2 | * * N | 0 1 1
---------+-----+-------+------
x.No.    ♦ N 0 | N 0 0 | 1 * *
xx ..&#x | 2 2 | 1 2 1 | * N *
.xN.o    ♦ 0 N | 0 0 N | * * 1

xxNxx&#x     (N → ∞)   → 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

:x:&##x   (N → ∞)   → height = 1

 o      | 2N | 1  2 | 2 1
--------+----+------+----
 x      |  2 | N  * | 2 0
:o:&#x  |  2 | * 2N | 1 1
--------+----+------+----
:x:&#x  |  4 | 2  2 | N *
:o:&##x ♦  N | 0  N | * 2

:xx:&##x   (N → ∞)   → height(1,2) = height(2,1') = 1

 o.      | 2N  * | 1  1  1 0 | 1 1 1
 .o      |  * 2N | 0  1  1 1 | 1 1 1
---------+-------+-----------+------
 x.      |  2  0 | N  *  * * | 1 1 0
 oo &#x  |  1  1 | * 2N  * * | 1 0 1 inner
:oo:&#x  |  1  1 | *  * 2N * | 0 1 1 outer
 .x      |  0  2 | *  *  * N | 1 1 0
---------+-------+-----------+------
 xx &#x  |  2  2 | 1  2  0 1 | N * * inner
:xx:&#x  |  2  2 | 1  0  2 1 | * N * outer
:oo:&##x ♦  N  N | 0  N  N 0 | * * 2