Cutting a regular dodecahedron in half - Part 1
Geometry
Level
pending
A dodecahedron of unit edge length is cut in half by a cutting plane that is parallel to one of its faces. The cut face is a regular decagon. Find the side length of this regular decagon.
The answer is 0.809.
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1 solution
The sides of the decagon connect the midpoints of two adjacent sides of a pentagon. As such, their length is sin ( 5 4 o ) = 4 1 ( 1 + 5 ) ≈ 0 . 8 0 9 .