Acronym | spd{3,5,3} (old: spt{3,5,3}) |
Name | semi partial diminishing (old: truncation) of hyperbolic order 3 icosahedral tesselation |
Circumradius | sqrt[(1-3 sqrt(5))/22] = 0.509376 i |
Confer |
In fact, the ike cells in here have s3s3s symmetry. The vertex figure is a para-bidiminished doe, faceting a pair of antipodal vertices to the depth of just one reduced edge set, i.e. down to their neighbouring vertices: fxfo3ofxf&#xt. Note that the inclined polar and the parallel tropal edges of the verf get combined by the overall symmetry of the honeycomb.
The qualifier "semi" in here relates to a not so often partial diminishing of the starting honeycomb (in fact: one eleventh of its vertices), respectively to the vertex figure, than being used for pd{3,5,3}. As the vertex set in both cases is a mere subset of the original tesselation, the overall curvature still remains the same.
Incidence matrix according to Dynkin symbol
(N → ∞) 10N | 6 12 | 6 18 6 | 2 6 6 -----+---------+-------------+-------- 2 | 30N * | 2 2 0 | 1 2 1 2 | * 60N | 0 2 1 | 0 1 2 -----+---------+-------------+-------- 5 | 5 0 | 12N * * | 1 1 0 3 | 1 2 | * 60N * | 0 1 1 3 | 0 3 | * * 20N | 0 0 2 -----+---------+-------------+-------- ♦ 20 | 30 0 | 12 0 0 | N * * ♦ 10 | 10 10 | 2 10 0 | * 6N * ♦ 12 | 6 24 | 0 12 8 | * * 5N
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