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Elongated Pentagonal Orthocupola's vertices (Posted on 2017-03-20) Difficulty: 2 of 5
An Elongated Pentagonal Orthocupolarotunda (one of the 92 Johnson solids) has 37 faces, 15 of which are squares, 7 of which are regular pentagons, and 15 of which are triangles.

How many vertices does it have?

No Solution Yet Submitted by Ady TZIDON    
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solution | Comment 1 of 3
from Eulers formula we have
F+V-E=2
where
F: number of faces
V: number of vertices
E: number of edges

F=37
E=4*15+7*5+15*3=140

Thus
37+V-140=2
V=105

Thus there are 105 vertices

  Posted by Daniel on 2017-03-20 11:21:34
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