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?
from Eulers formula we have
F+VE=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+V140=2
V=105
Thus there are 105 vertices

Posted by Daniel
on 20170320 11:21:34 