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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
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List of polyhedra

Platonic polyhedra

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

Archimedes and Catalan polyhedra

Name 3D model Video Dual Immersive rooms
U2 Truncated tetrahedron 3D model video dual Archimedes
immersive room
Catalan
immersive room
Triakis Tetrahedron 3D model video
U7 Cuboctahedron 3D model video dual
Rhombic Dodecahedron 3D model video
U8 Truncated octahedron 3D model video dual
Tetrakis Hexahedron 3D model video
U9 Truncated cube 3D model video dual
Triakis Octahedron 3D model video
U10 Rhombicuboctahedron 3D model video dual
Deltoidal Icositetrahedron 3D model video
U11 Truncated cuboctahedron 3D model video dual
Disdyakis Dodecahedron 3D model video
U12 Snub cube 3D model video dual
Pentagonal Icositetrahedron 3D model video
U24 Icosidodecahedron 3D model video dual
Rhombic Triacontahedron 3D model video
U25 Truncated icosahedron 3D model video dual
Pentakis Dodecahedron 3D model video
U26 Truncated dodecahedron 3D model video dual
Triakis Icosahedron 3D model video
U27 Rhombicosidodecahedron 3D model video dual
Deltoidal Hexecontahedron 3D model video
U28 Truncated icosidodecahedron 3D model video dual
Disdyakis Triacontahedron 3D model video
U29 Snub dodecahedron 3D model video dual
Pentagonal Hexecontahedron 3D model video
Duality 3D model video

Nonconvex polyhedra

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

Pyramids, tetrahedrons, prisms and antiprisms

Name 3D model Video Immersive rooms
U76 Prism 3D model video immersive room
U77 Antiprism 3D model video
U78 Stellated Prism 3D model video
U79 Stellated Antiprism 3D model video
U80 Stellated Crossed Antiprism 3D model video
Pyramid 3D model video
Stellated Pyramid 3D model video
Dipyramid 3D model video
Stellated Dipyramid 3D model video
Trapezohedron 3D model video
Stellated Trapezohedron 3D model video
Stellated Concave Trapezohedron 3D model video
Isosceles tetrahedron 3D model video
Non convex Hexakis Tetrahedron 3D model video
Non convex Hexakis Tetrahedron v2 3D model video
Trapezo-rhombic Dodecahedron 3D model video immersive room
Octahedral Pentagonal Dodecahedron 3D model video
Concave Dyakis Dodecahedron 3D model video
Dyakis Dodecahedron 3D model video
Tetragonal Pentagonal Dodecahedron 3D model video
Hexakis Tetrahedron 3D model video
Trapezohedral Tristetrahedron 3D model video
Iris Toroid 3D model video
Iris Antitoroid 3D model video
Rhombic enneacontahedron 3D model video
Goddard-Henning enneahedron 3D model video
Herschel enneahedron 3D model video
Parallelepiped 3D model video
Non convex Hexakis Tetrahedron v3 3D model video
Convex Trapezohedral Tristetrahedron 3D model video

Self-intersecting polyhedra

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

Quasi regular polyhedra

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

Self-intersecting truncated polyhedra

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

Self-intersecting snub polyhedra

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

Johnson solids

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


Licença Creative Commons
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.

DOI


References:
Weisstein, Eric W. “Archimedean Solid” From MathWorld-A Wolfram Web Resource. http://mathworld.wolfram.com/ArchimedeanSolid.html
Weisstein, Eric W. “Platonic Solid” From MathWorld-A Wolfram Web Resource. http://mathworld.wolfram.com/PlatonicSolid.html
Weisstein, Eric W. “Archimedean Dual” From MathWorld-A Wolfram Web Resource. https://mathworld.wolfram.com/ArchimedeanDual.html
Weisstein, Eric W. “Uniform Polyhedron.” From MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/UniformPolyhedron.html
Wikipedia https://en.wikipedia.org/wiki/Archimedean_solid
Wikipedia https://en.wikipedia.org/wiki/Platonic_solid
McCooey, David I. “Visual Polyhedra”. http://dmccooey.com/polyhedra/