Visualization of Polyhedra with Virtual Reality (VR) in A-frame
author: Paulo Henrique Siqueira - Universidade Federal do Paraná
contact: paulohscwb@gmail.com
versão em português
Cube family
A polyhedral compound is an arrangement of several interpenetrating polyhedra, all the same or of distinct types. Polyhedral compounds often have visually interesting symmetrical properties. Compounds of multiple Platonic and Archimedean solids can be especially appealing, as can compounds of these solids and their duals.
This work shows polyhedral compounds, modeled for viewing in Virtual Reality.
3D models
1. Concave Dodecahedron
The chiricosahedron is composed of five polyhedra and can be considered regular. In this compound, we have the vertices of the five chosen polyhedra forming a convex hull with common vertices, or with correspondence with the faces of a regular dodecahedron.
2. Concave Dyakis Dodecahedron
The result of “Compound 1” of 3 polyhedra is a stellated polyhedron, resembling stellated pyramids.
3. Cube
The result of “Compound 2” of 3 polyhedra is a stellated polyhedron, resembling stellated trapezohedrons.
4. Cube kites
The result of “Compound 3” of 5 polyhedra is a stellated polyhedron, resembling double stellated pyramids.
5. Cubitruncated Cuboctahedron
The result of “Compound 4” of 20 polyhedra is a stellated polyhedron, resembling Kepler-Poinsot polyhedra.
6. Cuboctahedron
The Escher compound can be adapted to the cube family using 5 polyhedra. The result of this composition is a solid that resembles the Escher solid. The central image of the 1948 engraving Stars popularized the Escher compound of octahedra.
7. Cubohemioctahedron
The disnubahedron is a compound of six polyhedra, with rotation angles of 30º or 45º, forming a uniform polyhedron.
8. Escher Solid
The snubahedron is a compound of three polyhedra, with rotation angles of 45º, forming a uniform polyhedron.
9. Escher Solid Dual
The chiricosahedron is composed of five polyhedra and can be considered regular. In this compound, we have the vertices of the five chosen polyhedra forming a convex hull with common vertices, or with correspondence with the faces of a regular dodecahedron.
10. Great Cubicuboctahedron
The result of “Compound 1” of 3 polyhedra is a stellated polyhedron, resembling stellated pyramids.
11. Great Deltoidal Icositetrahedron
The result of “Compound 2” of 3 polyhedra is a stellated polyhedron, resembling stellated trapezohedrons.
12. Great Disdyakis Dodecahedron
The chiricosahedron is composed of five polyhedra and can be considered regular. In this compound, we have the vertices of the five chosen polyhedra forming a convex hull with common vertices, or with correspondence with the faces of a regular dodecahedron.
13. Great Rhombihexacron
The Escher compound can be adapted to the cube family using 5 polyhedra. The result of this composition is a solid that resembles the Escher solid. The central image of the 1948 engraving Stars popularized the Escher compound of octahedra.
14. Great Rhombihexahedron
The result of “Compound 3” of 5 polyhedra is a stellated polyhedron, resembling double stellated pyramids.
15. Great Triakis Octahedron
The result of “Compound 4” of 20 polyhedra is a stellated polyhedron, resembling Kepler-Poinsot polyhedra.
16. Great Truncated Cuboctahedron
The snubahedron is a compound of three polyhedra, with rotation angles of 45º, forming a uniform polyhedron.
17. Joined Rhombicuboctahedron
The result of “Compound 1” of 3 polyhedra is a stellated polyhedron, resembling stellated pyramids.
18. Joined Snub Cube
The result of “Compound 4” of 20 polyhedra is a stellated polyhedron, resembling Kepler-Poinsot polyhedra.
19. Joined Truncated Octahedron
The chiricosahedron is composed of five polyhedra and can be considered regular. In this compound, we have the vertices of the five chosen polyhedra forming a convex hull with common vertices, or with correspondence with the faces of a regular dodecahedron.
20. Möbius Hexakis Octahedron
The Escher compound can be adapted to the cube family using 5 polyhedra. The result of this composition is a solid that resembles the Escher solid. The central image of the 1948 engraving Stars popularized the Escher compound of octahedra.
21. Möbius Octakis Hexahedron
The chiricosahedron is composed of five polyhedra and can be considered regular. In this compound, we have the vertices of the five chosen polyhedra forming a convex hull with common vertices, or with correspondence with the faces of a regular dodecahedron.
22. Octahemioctacron
The result of “Compound 4” of 20 polyhedra is a stellated polyhedron, resembling Kepler-Poinsot polyhedra.
23. Octahemioctahedron
The result of “Compound 2” of 3 polyhedra is a stellated polyhedron, resembling stellated trapezohedrons.
24. Rhombicuboctahedron
The result of “Compound 3” of 5 polyhedra is a stellated polyhedron, resembling double stellated pyramids.
25. Small Cubicuboctahedron
The result of “Compound 4” of 20 polyhedra is a stellated polyhedron, resembling Kepler-Poinsot polyhedra.
26. Small Rhombihexahedron
The Escher compound can be adapted to the cube family using 5 polyhedra. The result of this composition is a solid that resembles the Escher solid. The central image of the 1948 engraving Stars popularized the Escher compound of octahedra.
27. Snub Cube
The disnubahedron is a compound of six polyhedra, with rotation angles of 30º or 45º, forming a uniform polyhedron.
28. Stellated Truncated Hexahedron
The snubahedron is a compound of three polyhedra, with rotation angles of 45º, forming a uniform polyhedron.
29. Tetrakis Hexahedron
The chiricosahedron is composed of five polyhedra and can be considered regular. In this compound, we have the vertices of the five chosen polyhedra forming a convex hull with common vertices, or with correspondence with the faces of a regular dodecahedron.
30. Truncated Cube
The result of “Compound 4” of 20 polyhedra is a stellated polyhedron, resembling Kepler-Poinsot polyhedra.
31. Truncated Cuboctahedron
The disnubahedron is a compound of six polyhedra, with rotation angles of 30º or 45º, forming a uniform polyhedron.
32. Uniform Great Rhombicuboctahedron
The result of “Compound 1” of 3 polyhedra is a stellated polyhedron, resembling stellated pyramids.
33. Cuboctahedron Kites
The result of “Compound 4” of 20 polyhedra is a stellated polyhedron, resembling Kepler-Poinsot polyhedra.
34. Rhombicuboctahedron Kites
The chiricosahedron is composed of five polyhedra and can be considered regular. In this compound, we have the vertices of the five chosen polyhedra forming a convex hull with common vertices, or with correspondence with the faces of a regular dodecahedron.
35. Snub Cube Kites
The snubahedron is a compound of three polyhedra, with rotation angles of 45º, forming a uniform polyhedron.
36. Truncated Cube Kites
The disnubahedron is a compound of six polyhedra, with rotation angles of 30º or 45º, forming a uniform polyhedron.
37. Truncated Cuboctahedron Kites
The result of “Compound 3” of 5 polyhedra is a stellated polyhedron, resembling double stellated pyramids.
Polyhedral Compound - Cube family: visualization with 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., "Polyhedral Compound - Cube family: visualization with Virtual Reality". Available in: <https://paulohscwb.github.io/polycompound/compounds2/>, June 2025.
References:
Weisstein, Eric W. “Polyhedron Compound” From MathWorld-A Wolfram Web Resource. https://mathworld.wolfram.com/PolyhedronCompound.html
Weisstein, Eric W. “Uniform Polyhedron.” From MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/UniformPolyhedron.html
McCooey, David I. “Visual Polyhedra”. http://dmccooey.com/polyhedra/