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
Chamfered polyhedra
We define the operation of “chamfering” as a truncation along the edges of a polyhedron. A chamfered polyhedron, also known as an egde-truncated polyhedron, is a polyhedron constructed from an original polyhedron by moving faces outward while retaining the original vertices, thus creating a new hexagon, in general not regular, in place of each original edge. On this page we have Plato’s polyhedra and an Archimedes polyhedron “chamfered”. The polyhedra obtained with the chamfer operation have all edges of the same length.
Augmented Reality | 3D Models | Home
Immersive room
Augmented Reality
To view chamfered polyhedra in AR, simply visit:
https://paulohscwb.github.io/polyhedra2/chamfered/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.
3D models
1. Chamfered tetrahedron
A chamfered tetrahedron, also known as the alternate truncated cube, is a polyhedron obtained by chamfering a regular tetrahedron. An equilateral chamfered tetrahedron may be constructed by appropriate choice of the edge length ratio for chamfering.
Faces: 4 equilateral triangles and 6 mirror-symmetric hexagons | Edges: 24 | Vertices: 16. More…
2. Chamfered cube
A chamfered cube, also called truncated rhombic dodecahedron or tetratruncated rhombic dodecahedron, is a polyhedron obtained by chamfering a cube. An equilateral chamfered cube may be constructed by appropriate choice of the edge length ratio for chamfering.
Faces: 6 squares and 12 mirror-symmetric hexagons | Edges: 48 | Vertices: 32. More…
3. Chamfered octahedron
A chamfered octahedron, also called tritruncated rhombic dodecahedron, is a polyhedron obtained by chamfering a regular octahedron. An equilateral chamfered octahedron may be constructed by appropriate choice of the edge length ratio for chamfering.
Faces: 8 equilateral triangles and 12 mirror-symmetric hexagons | Edges: 48 | Vertices: 30. More…
4. Chamfered icosahedron
A chamfered icosahedron, also called a tritruncated rhombic triacontahedron, is a polyhedron obtained by chamfering a regular icosahedron. An equilateral chamfered icosahedron may be constructed by appropriate choice of the edge length ratio for chamfering.
Faces: 20 equilateral triangles and 30 mirror-symmetric hexagons | Edges: 120 | Vertices: 72. More…
5. Chamfered dodecahedron
A chamfered dodecahedron, also called truncated rhombic triacontahedron or pentatruncated rhombic triacontahedron, is a polyhedron obtained by chamfering a regular dodecahedron. An equilateral chamfered dodecahedron may be constructed by appropriate choice of the edge length ratio for chamfering.
Faces: 12 regular pentagons and 30 mirror-symmetric hexagons | Edges: 120 | Vertices: 80. More…
6. Chamfered truncated icosahedron
A chamfered truncated icosahedron is a polyhedron obtained by chamfering a regular truncated icosahedron. An equilateral chamfered truncated icosahedron may be constructed by appropriate choice of the edge length ratio for chamfering.
Faces: 12 regular pentagons, 20 regular hexagons and 90 mirror-symmetric hexagons | Edges: 360 | Vertices: 240. More…
Chamfered 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., "Chamfered polyhedra - Visualization of polyhedra with Augmented Reality and Virtual Reality". Available in: <https://paulohscwb.github.io/polyhedra2/chamfered/>, November 2023.
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. “Chamfered Polyhedron” From MathWorld-A Wolfram Web Resource. https://mathworld.wolfram.com/ChamferedPolyhedron.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/