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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

Archimedean and Catalan convex hulls

Each polyhedron on this page is the convex hull of an solid of Archimedes compounded with its Catalan dual. This operation is equivalent to John Conway’s ‘join’ operation applied to either the Archimedean solid or the respective Catalan dual.

Augmented Reality  |  3D Models  |  Home


Immersive room

VR immersive room to Archimedean and Catalan Convex Hulls🔗 room link


Augmented Reality

To view Archimedean and Catalan Convex Hulls in AR, simply visit:

https://paulohscwb.github.io/polyhedra2/ArchimedeanCatalanHulls/ra.html

with any browser with a webcam device (smartphone, tablet or notebook).
Access to the VR sites is done by clicking on the blue circle that appears on top of the marker.

Augmented Reality to Archimedean and Catalan Convex Hulls

Augmented Reality to Archimedean and Catalan Convex Hulls


3D models

1. Joined truncated tetrahedron

Joined Truncated Tetrahedron

The joined truncated tetrahedron is a composite of the Archimedean truncated tetrahedron with its respective dual, the Catalan triakis tetrahedron.
It has faces shaped like rhombi and kites.


Faces: 12 kites and 6 rhombi | Edges: 36 | Vertices: 20. More…


2. Joined Cuboctahedron

Joined Cuboctahedron

The joined cuboctahedron is a composite of the Archimedean cuboctahedron with its respective dual, the Catalan rhombic dodecahedron.
It has faces shaped like kites.


Faces: 24 kites | Edges: 48 | Vertices: 26. More…


3. Joined Truncated Octahedron

Joined Truncated Octahedron

The joined truncated octahedron is a composite of the Archimedean truncated octahedron with its respective dual, the Catalan tetrakis hexahedron.
It has faces shaped like rhombi and kites.


Faces: 24 kites and 12 rhombi | Edges: 72 | Vertices: 38. More…


4. Joined Truncated Cube

Joined Truncated Cube

The joined truncated cube is a composite of the Archimedean truncated cube with its respective dual, the Catalan triakis octahedron.
It has faces shaped like rhombi and kites.


Faces: 24 kites and 12 rhombi | Edges: 72 | Vertices: 38. More…


5. Joined Rhombicuboctahedron

Joined Rhombicuboctahedron

The joined rhombicuboctahedron is a composite of the Archimedean rhombicuboctahedron with its respective dual, the Catalan deltoidal icositetrahedron.
It has faces shaped like rhombi and kites.


Faces: 24 kites and 24 rhombi | Edges: 96 | Vertices: 50. More…


6. Joined Snub Cube

Joined Snub Cube

The joined snub cube is a composite of the Archimedean snub cube with its respective dual, the Catalan pentagonal icositetrahedron.
It has faces shaped like rhombi and kites.


Faces: 24 kites and 36 rhombi | Edges: 120 | Vertices: 62. More…


7. Joined Icosidodecahedron

Joined Icosidodecahedron

The joined icosidodecahedron is a composite of the Archimedean icosidodecahedron with its respective dual, the Catalan rhombic triacontahedron.
It has faces shaped like kites.


Faces: 60 kites | Edges: 120 | Vertices: 62. More…


8. Joined Truncated Cuboctahedron

Joined Truncated Cuboctahedron

The joined truncated cuboctahedron is a composite of the Archimedean truncated cuboctahedron with its respective dual, the Catalan disdyakis dodecahedron.
It has faces shaped like 24 short, 24 medium and 24 long kites.


Faces: 72 kites | Edges: 144 | Vertices: 74. More…


9. Joined Truncated Icosahedron

Joined Truncated Icosahedron

The joined truncated icosahedron is a composite of the Archimedean truncated icosahedron with its respective dual, the Catalan pentakis dodecahedron.
It has faces shaped like rhombi and kites.


Faces: 60 kites and 30 rhombi | Edges: 180 | Vertices: 92. More…


10. Joined Truncated Dodecahedron

Joined Truncated Dodecahedron

The joined truncated dodecahedron is a composite of the Archimedean truncated dodecahedron with its respective dual, the Catalan triakis icosahedron.
It has faces shaped like rhombi and kites.


Faces: 60 kites and 30 rhombi | Edges: 180 | Vertices: 92. More…


11. Joined Rhombicosidodecahedron

Joined Rhombicosidodecahedron

The joined rhombicosidodecahedron is a composite of the Archimedean rhombicosidodecahedron with its respective dual, the Catalan deltoidal hexecontahedron.
It has faces shaped like 60 short kites and 60 medium kites.


Faces: 120 kites | Edges: 240 | Vertices: 122. More…


12. Joined Snub Dodecahedron

Joined Snub Dodecahedron

The joined snub dodecahedron is a composite of the Archimedean snub dodecahedron with its respective dual, the Catalan pentagonal hexecontahedron.
It has faces shaped like kites and rhombi.


Faces: 60 kites and 90 rhombi | Edges: 300 | Vertices: 152. More…


13. Joined Truncated Icosidodecahedron

Joined Truncated Icosidodecahedron

The joined truncated icosidodecahedron is a composite of the Archimedean truncated icosidodecahedron with its respective dual, the Catalan disdyakis triacontahedron.
It has faces shaped like 60 short, 60 medium and 60 long kites.


Faces: 180 kites | Edges: 360 | Vertices: 182. More…

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Licença Creative Commons
Archimedean Catalan Convex Hulls - 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., "Archimedean Catalan Convex Hulls - Visualization of polyhedra with Augmented Reality and Virtual Reality". Available in: <https://paulohscwb.github.io/polyhedra2/ArchimedeanCatalanHulls/>, October 2023.

DOI

References:
Weisstein, Eric W. “Archimedean Solid” From MathWorld-A Wolfram Web Resource. http://mathworld.wolfram.com/ArchimedeanSolid.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
McCooey, David I. “Visual Polyhedra”. http://dmccooey.com/polyhedra/