Polytope Gallery

Regular Convex Polytopes

The 6 four-dimensional analogs of Platonic solids

• • 5-cell (Pentachoron)
• • 8-cell (Tesseract / Hypercube)
• • 16-cell (Hexadecachoron)
• • 24-cell (Icositetrachoron)
• • 120-cell (Hecatonicosachoron)
• • 600-cell (Hexacosichoron)

Uniform Polychora

Vertex-transitive polytopes with regular polygon faces

• • Cat 1-7: Pentachoric & Tesseractic families
• • Cat 8-17: Icositetrachoric family
• • Cat 18-26: Hecatonicosachoric families
• • Cat 30: Snub 24-cell family

~1,000 polytopes across 30 categories

Scaliform Polychora

Vertex-transitive with equal edge lengths but non-regular faces

• • CatS 1-6: Simple scaliforms & alterprisms
• • CatS 10-13: Podary & duoprismatic blends
• • CatS 18-19: Swirlprisms & exotic forms

~650 polytopes across 19 categories

Prismatic Polychora

4D prisms built from 3D polyhedra

• • Duoprisms (polygon × polygon)
• • Antiprism prisms
• • Polygon-polyhedron hybrids

Compound Polytopes

Multiple polytopes occupying the same space

• • Compound of 5 tesseracts
• • Compound of 120 pentachora
• • Stellated compounds

29 compound polytopes

Star Polychora

Non-convex polytopes with intersecting faces

• • Great grand stellated 120-cell
• • Grand 600-cell
• • Stellated icositetrachora