Spiky Soccer Balls: Generalized Polar Zonohedral Clusters

Year: 2025 Authors: Laura Marotta; Brian Redmond

Core claim

Removing circumscribability yields generalized polar zonohedral clusters whose faceted forms correspond to truncations of the icosahedron, with explicit relations among truncation, pyramid height, and edge ratios.

Topics

polar zonohedral clusters, Kleetopes of the dodecahedron, truncated icosahedron, soccer ball symmetry

Domains

polyhedra, zonohedra, Minkowski sum, truncation geometry, geometric sculpture, mathematical art, architectural form, craft fabrication

Methods

generalized cluster construction, faceting by adjacent poles, ratio derivation, paper-and-acrylic modeling

Media

colored transparent acrylic, tape, folded score-cut panels, 3D polyhedral models

Source status

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