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

Star kites

The polyhedra shown on this page are formed by kites, with some vertices coinciding with the polyhedra of Plato and Archimedes. The faces of the Stars kites are congruent, determining monohedral solids. The symmetries of faces, edges and vertices are the same as those of the respective polyhedra of Plato and Archimedes.
This work shows the Stars kites, modeled for viewing in Virtual Reality. The numbers of vertices Vk, edges Ek and faces Fk have the following relation to the numbers of vertices V, edges E and faces F (n sides) of Archimedes and Plato polyhedra:

Ek = 3·E; Vk = F + E + V; Fk = n·F.

3D Models  |  Home

RV star kitesRV star kites

3D models

1. Cube

Cubic star kites
We build a Star with kites with some vertices coinciding with the vertices of the cube: Cubic star kites.
faces: 24 | edges: 36 | vertices: 26

2. Octahedron

Octahedral star kites
Octahedral star kites.
faces: 24 | edges: 36 | vertices: 26

3. Icosahedron

Icosahedral star kites
Icosahedral star kites.
faces: 60 | edges: 90 | vertices: 62

4. Dodecahedron

Dodecahedral star kites
Dodecahedral star kites.
faces: 60 | edges: 90 | vertices: 62

5. Tetrahedron

Tetrahedral star kites
Tetrahedral star kites (also called trapezohedral tristetrahedron).
faces: 12 | edges: 18 | vertices: 14

6. Cuboctahedron

Cuboctahedral star kites
Cuboctahedral star kites.
faces: 48 | edges: 72 | vertices: 50

7. Icosidodecahedron

Icosidodecahedral star kites
Icosidodecahedral star kites.
faces: 120 | edges: 180 | vertices: 122

8. Rhombicosidodecahedron

Rhombicosidodecahedral star kites
Rhombicosidodecahedral star kites.
faces: 240 | edges: 360 | vertices: 242

9. Rhombicuboctahedron

Rhombicuboctahedral star kites
Rhombicuboctahedral star kites.
faces: 96 | edges: 144 | vertices: 98

10. Snub Cube

Snub cube star kites
Snub cube star kites.
faces: 120 | edges: 180 | vertices: 122

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11. Snub Dodecahedron

Dodecahedron snub star kites
Dodecahedron snub star kites.
faces: 300 | edges: 450 | vertices: 302

12. Truncated Cube

Truncated cube star kites
Truncated cube star kites.
faces: 72 | edges: 108 | vertices: 74

13. Truncated Cuboctahedron

Truncated Cuboctahedron star kites
Truncated cuboctahedron star kites.
faces: 144 | edges: 216 | vertices: 146

14. Truncated Dodecahedron

Truncated Dodecahedron star kites
Truncated dodecahedron star kites.
faces: 180 | edges: 270 | vertices: 182

15. Truncated Icosahedron

Truncated Icosahedron star kites
Truncated icosahedron star kites.
faces: 180 | edges: 270 | vertices: 182

16. Truncated Icosidodecahedron

Truncated Icosidodecahedron star kites
Truncated icosidodecahedron star kites.
faces: 360 | edges: 540 | vertices: 362

17. Truncated Octahedron

Truncated octahedron star kites
Truncated octahedron star kites.
faces: 72 | edges: 108 | vertices: 74

18. Truncated Tetrahedron

Truncated Tetrahedron star kites
Truncated tetrahedron star kites.
faces: 36 | edges: 54 | vertices: 38

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Licença Creative Commons
Star kites: polyhedra and 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., "Star kites: polyhedra and visualization with Virtual Reality". Available in: <https://paulohscwb.github.io/polyhedra3/kites/>, June 2025.



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