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
Octahedra 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. Biscribed hexpropellor cube
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. Biscribed orthokis propellor cube
The result of “Compound 1” of 3 polyhedra is a stellated polyhedron, resembling stellated pyramids.
3. Biscribed orthotruncated propellor octahedron
The result of “Compound 2” of 3 polyhedra is a stellated polyhedron, resembling stellated trapezohedrons.
4. Biscribed propellor cube
The result of “Compound 3” of 5 polyhedra is a stellated polyhedron, resembling double stellated pyramids.
5. Biscribed propellor octahedron
The result of “Compound 4” of 20 polyhedra is a stellated polyhedron, resembling Kepler-Poinsot polyhedra.
6. Hexaedro tetrakis de hélice biscrito
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. Biscribed propellor truncated cuboctahedron
The disnubahedron is a compound of six polyhedra, with rotation angles of 30º or 45º, forming a uniform polyhedron.
8. Biscribed propellor truncated octahedron
The snubahedron is a compound of three polyhedra, with rotation angles of 45º, forming a uniform polyhedron.
9. Biscribed snub cube
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. Biscribed snub truncated octahedron
The result of “Compound 1” of 3 polyhedra is a stellated polyhedron, resembling stellated pyramids.
11. Biscribed truncated cuboctahedron
The result of “Compound 2” of 3 polyhedra is a stellated polyhedron, resembling stellated trapezohedrons.
12. Biscribed 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.
13. Chamfered cube
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. Chamfered octahedron
The result of “Compound 3” of 5 polyhedra is a stellated polyhedron, resembling double stellated pyramids.
15. Deltoidal icositetrahedron
The result of “Compound 4” of 20 polyhedra is a stellated polyhedron, resembling Kepler-Poinsot polyhedra.
16. Disdyakis dodecahedron
The snubahedron is a compound of three polyhedra, with rotation angles of 45º, forming a uniform polyhedron.
17. Dyakis dodecahedron
The result of “Compound 1” of 3 polyhedra is a stellated polyhedron, resembling stellated pyramids.
18. Great hexacronic icositetrahedron
The result of “Compound 4” of 20 polyhedra is a stellated polyhedron, resembling Kepler-Poinsot polyhedra.
19. Jessens orthogonal icosahedron
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. Joined truncated cube
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. Joined truncated cuboctahedron
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. Möbius hexakis octahedron
The result of “Compound 4” of 20 polyhedra is a stellated polyhedron, resembling Kepler-Poinsot polyhedra.
23. Möbius octakis hexahedron dual
The result of “Compound 2” of 3 polyhedra is a stellated polyhedron, resembling stellated trapezohedrons.
24. Octahedron
The result of “Compound 3” of 5 polyhedra is a stellated polyhedron, resembling double stellated pyramids.
25. Octahedron kites
The result of “Compound 4” of 20 polyhedra is a stellated polyhedron, resembling Kepler-Poinsot polyhedra.
26. Pentagonal icositetrahedron
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. Propellor cube
The disnubahedron is a compound of six polyhedra, with rotation angles of 30º or 45º, forming a uniform polyhedron.
28. Propellor octahedron
The snubahedron is a compound of three polyhedra, with rotation angles of 45º, forming a uniform polyhedron.
29. Propellor snub cube
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. Propellor tetrakis hexahedron
The result of “Compound 4” of 20 polyhedra is a stellated polyhedron, resembling Kepler-Poinsot polyhedra.
31. Propellor truncated cuboctahedron
The disnubahedron is a compound of six polyhedra, with rotation angles of 30º or 45º, forming a uniform polyhedron.
32. Propellor truncated octahedron
The result of “Compound 1” of 3 polyhedra is a stellated polyhedron, resembling stellated pyramids.
33. Rhombic dodecahedron
The result of “Compound 4” of 20 polyhedra is a stellated polyhedron, resembling Kepler-Poinsot polyhedra.
34. Small hexacronic icositetrahedron
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. Tetradyakis hexahedron
The snubahedron is a compound of three polyhedra, with rotation angles of 45º, forming a uniform polyhedron.
36. Tetrahemihexacron
The disnubahedron is a compound of six polyhedra, with rotation angles of 30º or 45º, forming a uniform polyhedron.
37. Tetrahemihexahedron
The result of “Compound 3” of 5 polyhedra is a stellated polyhedron, resembling double stellated pyramids.
38. Triakis octahedron
The result of “Compound 3” of 5 polyhedra is a stellated polyhedron, resembling double stellated pyramids.
39. Truncated octahedron
The result of “Compound 3” of 5 polyhedra is a stellated polyhedron, resembling double stellated pyramids.
40. Truncated octahedron kites
The result of “Compound 3” of 5 polyhedra is a stellated polyhedron, resembling double stellated pyramids.
Polyhedral Compound - Octahedra 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 - Octahedra family: visualization with Virtual Reality". Available in: <https://paulohscwb.github.io/polycompound/compounds3/>, February 2026.
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/