MathDB
TOT 255 1990 Spring O S3 combo geo with dodecahedron , icosahedron

Source:

June 8, 2024
geometry3D geometryicosahedrondodecahedron

Problem Statement

(a) Some vertices of a dodecahedron are to be marked so that each face contains a marked vertex. What is the smallest number of marked vertices for which this is possible?
(b) Answer the same question, but for an icosahedron.
(G. Galperin, Moscow)
(Recall that a dodecahedron has 1212 pentagonal faces which meet in threes at each vertex, while an icosahedron has 2020 triangular faces which meet in fives at each vertex.)