A Polyhedral Byway

Year: 2001 Authors: Paul Gailiunas

Core claim

By modifying familiar polyhedra through specific geometric cuts and joins, one can generate a rich family of polyhedra with concave pentagonal faces and other regular faces, including some with unexpectedly low symmetry and strong visual appeal.

Topics

polyhedra, concave pentagons, geometric dissections, symmetry, solid geometry

Domains

geometry, polyhedral combinatorics, symmetry groups, Euler’s formula, mathematical art, visual design, spatial construction, craft-based modeling

Methods

polyhedral cutting, fitting and joining pieces, translation of solids, convex hull construction, layered assembly

Media

cardboard polygons, latex cement, Mathematic Activity Tiles (MATs), Zometool

Source status

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