Angular Solids
Comprehensive collection of calculators for angular and polyhedral shapes in 3D geometry
Basic Angular Forms
Prisms and Antiprisms
Wedges and Angular Cuts
Special Angular Forms
Trapezohedra
Stellated Polyhedra
About Angular Solids
Angular solids are three-dimensional shapes bounded by flat polygonal faces, representing fundamental forms in geometry and practical applications:
- Architecture - Buildings, structural elements
- Engineering - Machine parts, frameworks
- Crystallography - Crystal structures, minerals
- Mathematics - Geometric theory, topology
- Manufacturing - Packaging, containers
- Gaming - Dice, game pieces
Fundamental Properties
Euler's Formula
(Vertices - Edges + Faces = 2)
Convex Polyhedra
No self-intersections
Regular Polyhedra
All faces and angles identical
Star Polyhedra
Self-intersecting forms
Practical Applications
Architecture & Construction
- Buildings: Rectangular structures, optimal space usage
- Roofing: Triangular and prismatic forms
- Foundations: Cubic and rectangular bases
Manufacturing & Design
- Packaging: Boxes, containers, efficient storage
- Machine Parts: Gears, brackets, structural components
- Furniture: Tables, cabinets, modular systems
Science & Research
- Crystallography: Mineral and crystal structures
- Chemistry: Molecular geometries and lattices
- Physics: Particle arrangements and symmetries
Entertainment & Education
- Gaming: Dice, board game pieces
- Puzzles: 3D geometric puzzles and toys
- Art: Sculptures and geometric installations
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Quick Reference
Historical Context
Ancient Greece (5th century BC): Plato associated regular polyhedra with classical elements.
Euclid (ca. 300 BC): Proved there are exactly five regular convex polyhedra.
Kepler (1619): Discovered the four regular star polyhedra.
Modern Era: Applications in crystallography, architecture, and computer graphics.
Classification
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