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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

Diamond polyhedra

The polyhedra on this page were created by joining right pyramids with other whole or truncated polyhedra. In this way, we obtain the diamond polyhedra.

Augmented Reality  |  3D Models  |  Home


Immersive rooms

🔗 room 1  |  🔗 room 2  |  🔗 room 3


Augmented Reality

To view diamond polyhedra in AR, simply visit:

https://paulohscwb.github.io/polyhedra2/diamonds/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 diamonds polyhedra

Augmented Reality to diamonds polyhedra


3D models

1. Diamond triangular cupola

Diamond Triangular Cupola

When we construct a right pyramid with a hexagonal base, which has the base coincident with the hexagonal face of a Johnson triangular cupola, we obtain a diamond triangular cupola.

Faces: 10 triangles and 3 squares | Edges: 21 | Vertices: 10. More…


2. Diamond square cupola

Diamond Square Cupola

When we construct a right pyramid with a octagonal base, which has the base coincident with the octagonal face of a Johnson square cupola, we obtain a diamond square cupola.

Faces: 12 triangles and 5 squares | Edges: 28 | Vertices: 13. More…


3. Diamond pentagonal cupola

Diamond Pentagonal Cupola

When we construct a right pyramid with a decagonal base, which has the base coincident with the decagonal face of a Johnson pentagonal cupola, we obtain a diamond pentagonal cupola.

Faces: 15 triangles, 5 squares and 1 pentagon | Edges: 35 | Vertices: 16. More…


4. Diamond pentagonal rotunda

Diamond Pentagonal rotunda

When we construct a right pyramid with a decagonal base, which has the base coincident with the decagonal face of a Johnson pentagonal rotunda, we obtain a diamond pentagonal rotunda.

Faces: 20 triangles and 6 pentagons | Edges: 45 | Vertices: 21. More…


5. Diamond pentagonal dipyramid

Diamond Pentagonal dipyramid

If we construct a dipyramid using two right pentagonal pyramids with different heights, we obtain a diamond pentagonal dipyramid.

Faces: 10 triangles | Edges: 15 | Vertices: 7. More…


6. Diamond hexagonal dipyramid

Diamond Hexagonal dipyramid

If we construct a dipyramid using two right hexagonal pyramids with different heights, we obtain a diamond hexagonal dipyramid.

Faces: 12 triangles | Edges: 18 | Vertices: 8. More…


7. Diamond heptagonal dipyramid

Diamond Heptagonal dipyramid

If we construct a dipyramid using two right heptagonal pyramids with different heights, we obtain a diamond heptagonal dipyramid.

Faces: 14 triangles | Edges: 21 | Vertices: 9. More…


8. Diamond octagonal dipyramid

Diamond Octagonal dipyramid

If we construct a dipyramid using two right octagonal pyramids with different heights, we obtain a diamond octagonal dipyramid.


Faces: 16 triangles | Edges: 24 | Vertices: 10. More…


9. Diamond square antiprism

Diamond Square antiprism

Consider a modified antiprism, with a square base reduced by a factor between 0.6 and 0.8. If we construct a right square pyramid with the base coinciding with the largest base of the antiprism, we obtain a diamond square antiprism.

Faces: 12 triangles and 1 square | Edges: 20 | Vertices: 9. More…


10. Diamond pentagonal antiprism

Diamond Pentagonal antiprism

Consider a modified antiprism, with a pentagonal base reduced by a factor between 0.6 and 0.8. If we construct a right pentagonal pyramid with the base coinciding with the largest base of the antiprism, we obtain a diamond pentagonal antiprism.

Faces: 15 triangles and 1 pentagon | Edges: 25 | Vertices: 11. More…


11. Diamond hexagonal antiprism

Diamond Hexagonal antiprism

Consider a modified antiprism, with a hexagonal base reduced by a factor between 0.6 and 0.8. If we construct a right hexagonal pyramid with the base coinciding with the largest base of the antiprism, we obtain a diamond hexagonal antiprism.

Faces: 18 triangles and 1 hexagon | Edges: 30 | Vertices: 13. More…


12. Diamond heptagonal antiprism

Diamond Heptagonal antiprism

Consider a modified antiprism, with a heptagonal base reduced by a factor between 0.6 and 0.8. If we construct a right heptagonal pyramid with the base coinciding with the largest base of the antiprism, we obtain a diamond heptagonal antiprism.

Faces: 21 triangles and 1 heptagon | Edges: 35 | Vertices: 15. More…


13. Diamond octagonal antiprism

Diamond Octagonal antiprism

Consider a modified antiprism, with a octagonal base reduced by a factor between 0.6 and 0.8. If we construct a right octagonal pyramid with the base coinciding with the largest base of the antiprism, we obtain a diamond octagonal antiprism.

Faces: 24 triangles and 1 octagon | Edges: 40 | Vertices: 17. More…


14. Diamond mirror square antiprism

Diamond mirror square antiprism

Consider a modified antiprism, with a square base reduced by a factor between 0.6 and 0.8. Find the reflection of the smaller base of the antiprism relative to the larger base. By joining the vertex of a right square pyramid with the vertices of the largest base and the reflected antiprism base, we find a diamond mirror square antiprism.

Faces: 20 triangles and 1 square | Edges: 32 | Vertices: 13. More…


15. Diamond mirror pentagonal antiprism

Diamond mirror pentagonal antiprism

Consider a modified antiprism, with a pentagonal base reduced by a factor between 0.6 and 0.8. Find the reflection of the smaller base of the antiprism relative to the larger base. By joining the vertex of a right pentagonal pyramid with the vertices of the largest base and the reflected antiprism base, we find a diamond mirror pentagonal antiprism.

Faces: 25 triangles and 1 pentagon | Edges: 40 | Vertices: 16. More…


16. Diamond mirror hexagonal antiprism

Diamond mirror hexagonal antiprism

Consider a modified antiprism, with a hexagonal base reduced by a factor between 0.6 and 0.8. Find the reflection of the smaller base of the antiprism relative to the larger base. By joining the vertex of a right hexagonal pyramid with the vertices of the largest base and the reflected antiprism base, we find a diamond mirror hexagonal antiprism.

Faces: 30 triangles and 1 hexagon | Edges: 48 | Vertices: 19. More…


17. Diamond mirror heptagonal antiprism

Diamond mirror heptagonal antiprism

Consider a modified antiprism, with a heptagonal base reduced by a factor between 0.6 and 0.8. Find the reflection of the smaller base of the antiprism relative to the larger base. By joining the vertex of a right heptagonal pyramid with the vertices of the largest base and the reflected antiprism base, we find a diamond mirror heptagonal antiprism.

Faces: 35 triangles and 1 heptagon | Edges: 56 | Vertices: 22. More…


18. Diamond mirror octagonal antiprism

Diamond mirror octagonal antiprism

Consider a modified antiprism, with a octagonal base reduced by a factor between 0.6 and 0.8. Find the reflection of the smaller base of the antiprism relative to the larger base. By joining the vertex of a right octagonal pyramid with the vertices of the largest base and the reflected antiprism base, we find a diamond mirror octagonal antiprism.

Faces: 40 triangles and 1 octagon | Edges: 64 | Vertices: 25. More…


19. Augmented tridiminished icosahedron

Augmented tridiminished icosahedron

Johnson’s augmented tridiminished icosahedron can be considered a diamond polyhedron. It can be constructed by attaching a tetrahedron, seen as a triangular pyramid, to the triangular face of the tridiminished icosahedron which is connected only to the pentagons. It is the only Johnson solid that is constructed using decrease and increase, assuming that no decrease and increase cancel each other out.

Faces: 7 triangles and 3 pentagons | Edges: 18 | Vertices: 10. More…


20. Diamond augmented truncated tetrahedron

Diamond augmented truncated tetrahedron

When we construct a right pyramid with a triangular base, which has a base coinciding with a triangular face opposite the triangular cupola, we obtain a diamond augmented truncated tetrahedron.

Faces: 10 triangles, 3 squares and 3 hexagons | Edges: 30 | Vertices: 16. More…


21. Diamond truncated snub square antiprism

Diamond snub square antiprism

When we construct a right pyramid with an octagonal base, joining the apex vertex of this pyramid with the 8 vertices of one of the symmetrical parts of a snub square antiprism, we obtain a diamond truncated snub square antiprism.

Faces: 20 triangles and 1 square | Edges: 32 | Vertices: 13. More…


22. Diamond triangular hebesphenorotunda

Diamond triangular hebesphenorotunda

When we construct a right pyramid with a hexagonal base, which has the base coinciding with the hexagonal face of a triangular hebesphenorotunda, we obtain a diamond triangular hebesphenorotunda.

Faces: 19 triangles, 3 squares and 3 pentagons | Edges: 42 | Vertices: 19. More…


23. Diamond truncated triangular hebesphenorotunda

Diamond truncated triangular hebesphenorotunda

Consider a modified triangular hebesphenorotunda, disregarding the hexagonal face and all other faces that are joined with the hexagon vertices. The solid obtained by joining a right pyramid with an enneagonal base with the other faces of the modified triangular hebesphenorotunda is a diamond truncated triangular hebesphenorotunda.

Faces: 13 triangles and 3 pentagons | Edges: 27 | Vertices: 13. More…


24. Diamond truncated triangular hebesphenorotunda

Diamond truncated triangular hebesphenorotunda

Consider a modified triangular hebesphenorotunda, disregarding the pentagonal faces and the triangular face that is joined only with the pentagons vertices. The solid obtained by joining a right pyramid with an enneagonal base with the other faces of the modified triangular hebesphenorotunda is a diamond truncated triangular hebesphenorotunda.

Faces: 18 triangles, 3 squares and 1 hexagon | Edges: 36 | Vertices: 16. More…


25. Diamond truncated dodecahedron

Diamond truncated dodecahedron

Consider a modified dodecahedron, disregarding one face and the 5 faces that are joined with this disregarded face. The solid obtained by joining a right decagonal pyramid with a the other faces of the modified dodecahedron is a diamond truncated dodecahedron.

Faces: 10 triangles and 6 pentagons | Edges: 30 | Vertices: 16. More…


26. Diamond truncated square pyramid

Diamond truncated square pyramid

When we construct a right square pyramid, which has the base coinciding with the base of a truncated square pyramid, we obtain a diamond truncated square pyramid.

Faces: 4 triangles, 1 square and 4 trapezoids | Edges: 16 | Vertices: 9. More…


27. Diamond truncated pentagonal pyramid

Diamond truncated pentagonal pyramid

When we construct a right pentagonal pyramid, which has the base coinciding with the base of a truncated pentagonal pyramid, we obtain a diamond truncated pentagonal pyramid.

Faces: 5 triangles, 1 pentagon and 5 trapezoids | Edges: 20 | Vertices: 11. More…


28. Diamond truncated hexagonal pyramid

Diamond truncated hexagonal pyramid

When we construct a right hexagonal pyramid, which has the base coinciding with the base of a truncated hexagonal pyramid, we obtain a diamond truncated hexagonal pyramid.

Faces: 6 triangles, 1 hexagon and 6 trapezoids | Edges: 24 | Vertices: 13. More…


29. Diamond truncated heptagonal pyramid

Diamond truncated heptagonal pyramid

When we construct a right heptagonal pyramid, which has the base coinciding with the base of a truncated heptagonal pyramid, we obtain a diamond truncated heptagonal pyramid.

Faces: 7 triangles, 1 heptagon and 7 trapezoids | Edges: 28 | Vertices: 15. More…


30. Diamond truncated octagonal pyramid

Diamond truncated octagonal pyramid

When we construct a right octagonal pyramid, which has the base coinciding with the base of a truncated octagonal pyramid, we obtain a diamond truncated octagonal pyramid.

Faces: 8 triangles, 1 octagon and 8 trapezoids | Edges: 32 | Vertices: 17. More…


31. Diamond truncated disdyakis dodecahedron

Diamond truncated disdyakis dodecahedron

When we construct a right octagonal pyramid, with its main vertex united with the truncated Catalan disdiakis dodecahedron vertices, we obtain a diamond truncated disdiakis dodecahedron.

Faces: 32 triangles | Edges: 48 | Vertices: 18. More…


32. Diamond truncated triakis icosahedron

Diamond truncated triakis icosahedron

When we construct a right decagonal pyramid, with its main vertex united with the truncated Catalan triakis icosahedron vertices, we obtain a diamond truncated triakis icosahedron.

Faces: 30 triangles | Edges: 45 | Vertices: 17. More…


33. Diamond truncated pentakis dodecahedron

Diamond truncated pentakis dodecahedron

When we construct a right decagonal pyramid, with its main vertex united with the truncated Catalan pentakis dodecahedron vertices, we obtain a diamond truncated pentakis dodecahedron.

Faces: 30 triangles | Edges: 45 | Vertices: 17. More…


34. Diamond truncated pentagonal hexecontahedron

Diamond truncated pentagonal hexecontahedron

When we construct a right pentadecagonal pyramid, with its main vertex united with the truncated Catalan pentagonal hexecontahedron vertices, we obtain a diamond truncated pentagonal hexecontahedron.

Faces: 15 triangles and 15 pentagons | Edges: 60 | Vertices: 32. More…

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Licença Creative Commons
Diamond 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., "Diamond polyhedra - Visualization of polyhedra with Augmented Reality and Virtual Reality". Available in: <https://paulohscwb.github.io/polyhedra2/diamonds/>, November 2023.

DOI

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. “Uniform Polyhedron.” From MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/UniformPolyhedron.html
Weisstein, Eric W. “Johnson Solid” From MathWorld-A Wolfram Web Resource. https://mathworld.wolfram.com/JohnsonSolid.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/