Johnson Solids
Convex polyhedra with regular faces that are neither Platonic nor Archimedean
Pyramids
Cupolas and Rotundas
Elongated Forms
Bipyramids
Complex Johnson Forms
About Johnson Solids
Johnson solids are convex polyhedra with regular faces that don't fit into other well-known categories:
- Architecture - Complex building forms
- Engineering - Specialized components
- Crystallography - Unusual crystal forms
- Mathematics - Polyhedral theory
- 3D Modeling - Complex shapes
- Education - Geometric examples
Johnson Solid Properties
Regular Faces
(triangles, squares, pentagons, etc.)
Convexity
No concave surfaces
Non-Uniform
Different vertex types
Completeness
Enumerated by Norman Johnson
Categories and Applications
Pyramids & Bipyramids
- Architecture: Roof structures, spires
- Engineering: Structural joints
- Art: Sculptural forms
Cupolas & Rotundas
- Architecture: Dome structures
- Engineering: Pressure vessels
- Design: Decorative elements
Elongated Forms
- Manufacturing: Container shapes
- Architecture: Extended structures
- Packaging: Specialized containers
Complex Forms
- Research: Mathematical models
- 3D Printing: Test geometries
- Education: Geometry examples
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Quick Reference
Historical Context
Norman Johnson (1966): Systematically enumerated all 92 convex polyhedra with regular faces.
Victor Zalgaller (1969): Proved that Johnson's list of 92 solids was complete.
Modern Use: Applications in architecture, 3D modeling, and mathematical research.
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