perplexus.info :: Shapes : Elongated Pentagonal Orthocupola's vertices

Elongated Pentagonal Orthocupola's vertices (Posted on 2017-03-20)

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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