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

Even so 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

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

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

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