Polyhedra on an equilateral hyperboloid

Year: 2012 Authors: Dirk Huylebrouck

Core claim

Several crossed prisms and an extended hyperbolic cuboctahedron can be modeled on an equilateral hyperboloid, suggesting a poetic counterpart to Kepler’s spherical polyhedra.

Topics

hyperbolic polyhedra, ruled surfaces, tessellations, architectural geometry, mathematical art

Domains

hyperbolic geometry, polyhedra, Gaussian curvature, tessellations, conic sections, architecture, mathematical art, geometric design

Methods

geometric construction, surface revolution, comparative modeling, polyhedral extension, tessellation analogy

Media

hyperboloid, triangles, prisms, domes, drawings

Source status

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