Acronym ...
Name xfo3foo5oxf&#zx
 
Vertex figure [3,(5a)2], [3,5b,3,(5a)2], [(5a)3]
Dihedral angles
  • between {5a} and {5a} at type 2 edges:   360°-arccos(-1/sqrt(5)) = 243.434949°
  • between {3} and {5b}:   360°-arccos(-sqrt[(5+2 sqrt(5))/15]) = 217.377°
  • between {3} and {5a}:   arccos(-sqrt[(5-2 sqrt(5))/15]) = 100.812317°
  • between {5a} and {5a} at type 1 edges:   arccos(1/sqrt(5)) = 63.434949°

Excavating the type b pentagons by peppies would prolong the adjacent triangles into according rhombs. The thus obtained polyhedron xfoa3fooo5oxfo&zx then also occurs as the 41th stellation of the truncated icosahedron.


Incidence matrix according to Dynkin symbol

xfo3foo5oxf&#zx   → height = 0
(tegum sum of (x,f)-ti, (f,x)-srid, f-doe)

o..3o..5o..     | 60  *  * |  1   2  0  0 |  2  1  0  [3,(5a)2]
.o.3.o.5.o.     |  * 60  * |  0   2  2  1 |  2  2  1  [3,5b,3,(5a)2]
..o3..o5..o     |  *  * 20 |  0   0  0  3 |  3  0  0  [(5a)3]
----------------+----------+--------------+---------
x.. ... ...     |  2  0  0 | 30   *  *  * |  2  0  0  (type 1)
oo.3oo.5oo.&#x  |  1  1  0 |  * 120  *  * |  1  1  0
... ... .x.     |  0  2  0 |  *   * 60  * |  0  1  1
.oo3.oo5.oo&#x  |  0  1  1 |  *   *  * 60 |  2  0  0  (type 2)
----------------+----------+--------------+---------
xfo ... ...&#xt |  2  2  1 |  1   2  0  2 | 60  *  *  {5a}
... ... ox.&#xt |  1  2  0 |  0   2  1  0 |  * 60  *  {3}
... .o.5.x.     |  0  5  0 |  0   0  5  0 |  *  * 12  {5b}

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