Polyhedra

Visualization of polyhedra with Augmented Reality (AR) and Virtual Reality (VR) in A-frame

author: Paulo Henrique Siqueira - Universidade Federal do Paraná
contact: paulohscwb@gmail.com
versão em português
Home

List of polyhedra

Platonic polyhedra

Name		3D model	Video	Dual	Immersive room
U₁	Tetrahedron
U₅	Octahedron
U₆	Cube
U₂₂	Icosahedron
U₂₃	Dodecahedron
	Duality

Archimedes and Catalan polyhedra

Name		Immersive rooms
U₂	Truncated tetrahedron	Archimedes Catalan
	Triakis Tetrahedron
U₇	Cuboctahedron
	Rhombic Dodecahedron
U₈	Truncated octahedron
	Tetrakis Hexahedron
U₉	Truncated cube
	Triakis Octahedron
U₁₀	Rhombicuboctahedron
	Deltoidal Icositetrahedron
U₁₁	Truncated cuboctahedron
	Disdyakis Dodecahedron
U₁₂	Snub cube
	Pentagonal Icositetrahedron
U₂₄	Icosidodecahedron
	Rhombic Triacontahedron
U₂₅	Truncated icosahedron
	Pentakis Dodecahedron
U₂₆	Truncated dodecahedron
	Triakis Icosahedron
U₂₇	Rhombicosidodecahedron
	Deltoidal Hexecontahedron
U₂₈	Truncated icosidodecahedron
	Disdyakis Triacontahedron
U₂₉	Snub dodecahedron
	Pentagonal Hexecontahedron
	Duality

Nonconvex polyhedra

Name		3D model	Video	Dual	Immersive rooms
U₃	Octahemioctahedron
	Octahemioctacron
U₄	Tetrahemihexahedron
	Tetrahemihexacron
U₁₅	Cubohemioctahedron
	Hexahemioctacron
U₃₄	Small Stellated Dodecahedron
U₃₅	Great Dodecahedron
U₄₉	Small Icosihemidodecahedron
	Small icosihemidodecacron
U₅₁	Small Dodecahemidodecahedron
	Small dodecahemidodecacron
U₅₂	Great Stellated Dodecahedron
U₅₃	Great Icosahedron
U₆₂	Small Dodecahemicosahedron
	Small dodecahemicosacron
U₆₅	Great Dodecahemicosahedron
	Great dodecahemicosacron
U₇₀	Great Dodecahemidodecahedron
	Great dodecahemidodecacron
U₇₁	Great Icosihemidodecahedron
	Great icosihemidodecacron
	Escher's Solid
	Escher's Solid Dual
	Stella Octangula
	Rhombic Hexecontahedron
	Concave Dodecahedron
	Jessen's Orthogonal Icosahedron
	Möbius Deltahedron - 24 faces
	Möbius Deltahedron dual
	Möbius Octakis Hexahedron
	Möbius Octakis Hexahedron dual
	Möbius Hexakis Octahedron
	Möbius Hexakis Icosahedron
	Möbius 10-akis Dodecahedron
	Duality

Pyramids, tetrahedrons, prisms and antiprisms

Name		3D model	Video	Immersive rooms
U₇₆	Prism
U₇₇	Antiprism
U₇₈	Stellated Prism
U₇₉	Stellated Antiprism
U₈₀	Stellated Crossed Antiprism
	Pyramid
	Stellated Pyramid
	Dipyramid
	Stellated Dipyramid
	Trapezohedron
	Stellated Trapezohedron
	Stellated Concave Trapezohedron
	Isosceles tetrahedron
	Trapezo-rhombic Dodecahedron
	Octahedral Pentagonal Dodecahedron
	Concave Dyakis Dodecahedron
	Dyakis Dodecahedron
	Tetragonal Pentagonal Dodecahedron
	Hexakis Tetrahedron
	Trapezohedral Tristetrahedron
	Iris Toroid
	Iris Antitoroid
	Rhombic enneacontahedron
	Goddard-Henning enneahedron
	Herschel enneahedron
	Parallelepiped

Self-intersecting polyhedra

Name		3D model	Video	Dual	Immersive rooms
U₁₃	Small Cubicuboctahedron
	Small Hexacronic Icositetrahedron
U₁₄	Great Cubicuboctahedron
	Great Hexacronic Icositetrahedron
U₁₇	Uniform Great Rhombicuboctahedron
	Great Deltoidal Icositetrahedron
U₃₀	Small Ditrigonal Icosidodecahedron
	Small Triambic Icosahedron
U₃₁	Small icosicosidodecahedron
	Small icosacronic hexecontahedron
U₃₃	Small Dodecicosidodecahedron
	Small Dodecacronic Hexecontahedron
U₃₆	Dodecadodecahedron
	Medial Rhombic Triacontahedron
U₃₈	Rhombidodecadodecahedron
	Medial deltoidal hexecontahedron
U₄₁	Ditrigonal dodecahedron
	Medial Triambic Icosahedron
U₄₂	Great ditrigonal dodecicosidodecahedron
	Great ditrigonal dodecacronic hexecontahedron
U₄₃	Small ditrigonal dodecicosidodecahedron
	Small ditrigonal dodecacronic hexecontahedron
U₄₄	Icosidodecadodecahedron
	Medial icosacronic hexecontahedron
U₄₇	Great Ditrigonal Icosidodecahedron
	Great Triambic Icosahedron
U₄₈	Great Icosicosidodecahedron
	Great icosacronic hexecontahedron
U₅₄	Great Icosidodecahedron
	Great Rhombic Triacontahedron
U₆₁	Great Dodecicosidodecahedron
	Great dodecacronic hexecontahedron
U₆₇	Uniform great rhombicosidodecahedron
	Great deltoidal hexecontahedron
	Echidnahedron
	Duality

Quasi regular polyhedra

Name		3D model	Video	Dual	Immersive room
U₁₈	Small rhombihexahedron
	Small rhombihexacron
U₂₁	Great Rhombihexahedron
	Great Rhombihexacron
U₃₉	Small rhombidodecahedron
	Small rhombidodecacron
U₅₀	Small dodecicosahedron
	Small dodecicosacron
U₅₆	Rhombicosahedron
	Rhombicosacron
U₆₃	Great dodecicosahedron
	Great dodecicosacron
U₇₃	Great rhombidodecahedron
	Great rhombidodecacron
	Duality

Self-intersecting truncated polyhedra

Name		3D model	Video	Dual	Immersive rooms
U₁₆	Cubitruncated Cuboctahedron
	Tetradyakis Hexahedron
U₁₉	Stellated Truncated Hexahedron
	Great Triakis Octahedron
U₂₀	Great Truncated Cuboctahedron
	Great Disdyakis Dodecahedron
U₃₇	Truncated Great Dodecahedron
	Small Stellapentakis Dodecahedron
U₄₅	Icositruncated Dodecadodecahedron
	Tridyakis icosahedron
U₅₅	Great Truncated Icosahedron
	Great Stellapentakis Dodecahedron
U₅₈	Small Stellated Truncated Dodecahedron
	Great Pentakis Dodecahedron
U₅₉	Truncated Dodecadodecahedron
	Medial Disdyakis Triacontahedron
U₆₆	Great Stellated Truncated Dodecahedron
	Great Triakis Icosahedron
U₆₈	Great Truncated Icosidodecahedron
	Great Disdyakis Triacontahedron
	Duality

Self-intersecting snub polyhedra

Name		3D model	Video	Dual	Immersive rooms
U₃₂	Small Snub Icosicosidodecahedron
	Small Hexagonal Hexecontahedron
U₄₀	Snub Dodecadodecahedron
	Medial pentagonal hexecontahedron
U₄₆	Snub Icosidodecadodecahedron
	Medial Hexagonal Hexecontahedron
U₅₇	Great Snub Icosidodecahedron
	Great Pentagonal Hexecontahedron
U₆₀	Inverted Snub Dodecadodecahedron
	Medial inverted pentagonal hexecontahedron
U₆₄	Great Snub Dodecicosidodecahedron
	Great Hexagonal Hexecontahedron
U₆₉	Great Inverted Snub Icosidodecahedron
	Great Inverted Pentagonal Hexecontahedron
U₇₂	Small Retrosnub Icosicosidodecahedron
	Small Hexagrammic Hexecontahedron
U₇₄	Great Retrosnub Icosidodecahedron
	Great Pentagrammic Hexecontahedron
U₇₅	Great dirhombicosidodecahedron
	Great dirhombicosidodecacron
	Great Disnub Dirhombidodecahedron
	Duality

Johnson solids

Name		3D model	Video	Immersive rooms
J₁	Square pyramid
J₂	Pentagonal pyramid
J₃	Triangular cupola
J₄	Square cupola
J₅	Pentagonal cupola
J₆	Pentagonal rotunda
J₇	Elongated triangular pyramid
J₈	Elongated square pyramid
J₉	Elongated pentagonal pyramid
J₁₀	Gyroelongated square pyramid
J₁₁	Gyroelongated pentagonal pyramid
J₁₂	Triangular dipyramid
J₁₃	Pentagonal dipyramid
J₁₄	Elongated triangular dipyramid
J₁₅	Elongated square dipyramid
J₁₆	Elongated pentagonal dipyramid
J₁₇	Gyroelongated square dipyramid
J₁₈	Elongated triangular cupola
J₁₉	Elongated square cupola
J₂₀	Elongated pentagonal cupola
J₂₁	Elongated pentagonal rotunda
J₂₂	Gyroelongated triangular cupola
J₂₃	Gyroelongated square cupola
J₂₄	Gyroelongated pentagonal cupola
J₂₅	Gyroelongated pentagonal rotunda
J₂₆	Gyrobifastigium
J₂₇	Triangular orthobicupola
J₂₈	Square orthobicupola
J₂₉	Square gyrobicupola
J₃₀	Pentagonal orthobicupola
J₃₁	Pentagonal gyrobicupola
J₃₂	Pentagonal orthocupolarotunda
J₃₃	Pentagonal gyrocupolarotunda
J₃₄	Pentagonal orthobirotunda
J₃₅	Elongated triangular orthobicupola
J₃₆	Elongated triangular gyrobicupola
J₃₇	Elongated square gyrobicupola
J₃₈	Elongated pentagonal orthobicupola
J₃₉	Elongated pentagonal gyrobicupola
J₄₀	Elongated pentagonal orthocupolarotunda
J₄₁	Elongated pentagonal gyrocupolarotunda
J₄₂	Elongated pentagonal orthobirotunda
J₄₃	Elongated pentagonal gyrobirotunda
J₄₄	Gyroelongated triangular bicupola
J₄₅	Gyroelongated square bicupola
J₄₆	Gyroelongated pentagonal bicupola
J₄₇	Gyroelongated pentagonal cupolarotunda
J₄₈	Gyroelongated pentagonal birotunda
J₄₉	Gyroelongated pentagonal birotunda
J₅₀	Biaugmented triangular prism
J₅₁	Triaugmented triangular prism
J₅₂	Augmented pentagonal prism
J₅₃	Biaugmented pentagonal prism
J₅₄	Augmented hexagonal prism
J₅₅	Parabiaugmented hexagonal prism
J₅₆	Metabiaugmented hexagonal prism
J₅₇	Triaugmented hexagonal prism
J₅₈	Augmented dodecahedron
J₅₉	Parabiaugmented dodecahedron
J₆₀	Metabiaugmented dodecahedron
J₆₁	Triaugmented dodecahedron
J₆₂	Metabidiminished icosahedron
J₆₃	Tridiminished icosahedron
J₆₄	Augmented tridiminished icosahedron
J₆₅	Augmented truncated tetrahedron
J₆₆	Augmented truncated cube
J₆₇	Biaugmented truncated cube
J₆₈	Augmented truncated dodecahedron
J₆₉	Parabiaugmented truncated dodecahedron
J₇₀	Metabiaugmented truncated dodecahedron
J₇₁	Triaugmented truncated dodecahedron
J₇₂	Gyrate rhombicosidodecahedron
J₇₃	Parabigyrate rhombicosidodecahedron
J₇₄	Metabigyrate rhombicosidodecahedron
J₇₅	Trigyrate rhombicosidodecahedron
J₇₆	Diminished rhombicosidodecahedron
J₇₇	Paragyrate diminished rhombicosidodecahedron
J₇₈	Metagyrate diminished rhombicosidodecahedron
J₇₉	Bigyrate diminished rhombicosidodecahedron
J₈₀	Parabidiminished rhombicosidodecahedron
J₈₁	Metabidiminished rhombicosidodecahedron
J₈₂	Gyrate bidiminished rhombicosidodecahedron
J₈₃	Tridiminished rhombicosidodecahedron
J₈₄	Snub disphenoid
J₈₅	Snub square antiprism
J₈₆	Sphenocorona
J₈₇	Augmented sphenocorona
J₈₈	Sphenomegacorona
J₈₉	Hebesphenomegacorona
J₉₀	Disphenocingulum
J₉₁	Bilunabirotunda
J₉₂	Triangular hebesphenorotunda

Polyhedra: Visualization of polyhedra with Augmented Reality and Virtual Reality by Paulo Henrique Siqueira is licensed with a license Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International.

How to cite this work:

Siqueira, P.H., "Polyhedra: Visualization of polyhedra with Augmented Reality and Virtual Reality". Available in: <https://paulohscwb.github.io/polyhedra/>, September 2019.

References:
Weisstein, Eric W. “Uniform Polyhedron.” From MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/UniformPolyhedron.html
Weisstein, Eric W. “Miscellaneous Polyhedra” From MathWorld-A Wolfram Web Resource. http://mathworld.wolfram.com/topics/MiscellaneousPolyhedra.html
Weisstein, Eric W. “Johnson Solid” From MathWorld-A Wolfram Web Resource. https://mathworld.wolfram.com/JohnsonSolid.html
Wikipedia https://en.wikipedia.org/wiki/List_of_uniform_polyhedra
Wikipedia https://en.wikipedia.org/wiki/Johnson_solid
Polytope Miraheze https://polytope.miraheze.org/wiki/Johnson_solid
McCooey, David I. “Visual Polyhedra”. http://dmccooey.com/polyhedra/