Acronym | azap |
Name | apeirogonal antiprism |
© | |
Vertex figure | [3^{3},∞] |
Confer | |
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Although this looks just like a mere stripe of triangles, 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 antiprism, thereby becoming a flat tiling.
Incidence matrix according to Dynkin symbol
s2sNs (N → ∞) demi( . . . ) | 2N | 1 1 2 | 1 3 ---------------+----+--------+----- s2s . | 2 | N * * | 0 2 s . s2*a | 2 | * N * | 0 2 sefa( . sNs ) | 2 | * * 2N | 1 1 ---------------+----+--------+----- . sNs ♦ N | 0 0 N | 2 * sefa( s2sNs ) | 3 | 1 1 1 | * 2N starting figure: x xNx
s2s2No (N → ∞) demi( . . . ) | 2N | 2 2 | 1 3 ---------------+----+-------+----- s2s . | 2 | 2N * | 0 2 sefa( . s2No ) | 2 | * 2N | 1 1 ---------------+----+-------+----- . s2No ♦ N | 0 N | 2 * sefa( s2s2No ) | 3 | 2 1 | * 2N starting figure: x x2No
xoNox&#x (N → ∞) → height = sqrt(3)/2 = 0.866025
({N} || dual {N})
o.No. | N * | 2 2 0 | 1 2 1 0
.oN.o | * N | 0 2 2 | 0 1 2 1
---------+-----+--------+--------
x. .. | 2 0 | N * * | 1 1 0 0
ooNoo&#x | 1 1 | * 2N * | 0 1 1 0
.. .x | 0 2 | * * N | 0 0 1 1
---------+-----+--------+--------
x.No. ♦ N 0 | N 0 0 | 1 * * *
xo ..&#x | 2 1 | 1 2 0 | * N * *
.. ox&#x | 1 2 | 0 2 1 | * * N *
.oN.x ♦ 0 N | 0 0 N | * * * 1
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