# Euclid's Construction of a Regular Icosahedron (XIII.16)

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Let be a regular pentagon inscribed in circle * *with radius , and let , , , , and be the midpoints of the arcs , , , , and , respectively (step 2). is also a regular pentagon. The slider translates the pentagon in the direction normal to its plane up to the length of the radius * *(). Let and be the centers of and . The slider translates and , also in the direction normal to the plane , to its maximum value, which is the length of a side of the regular decagon inscribed in circle . The regular icosahedron is constructed by connecting corresponding points for maximum values of the sliders and .

Contributed by: Milana Dabic (October 2011)

Open content licensed under CC BY-NC-SA

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"Euclid's Construction of a Regular Icosahedron (XIII.16)"

http://demonstrations.wolfram.com/EuclidsConstructionOfARegularIcosahedronXIII16/

Wolfram Demonstrations Project

Published: October 19 2011