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
uniform relative:
x3o5o3o   pd{3,5,3}  

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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