View allAll Photos Tagged triacontahedron
You may have seen Dead Homer's version in the Lego Movie. Although I designed this a long time ago, it is essentially the *exact* same design as www.flickr.com/photos/deadhomer/15544266900/. This is one of my favorite polyhedra, the rhombic triacontahedron. This was made with 120 plate hinges, 60 1x2 with bar, 60 1x2 with two clips, 120 1x6 plates, and 120 1x6 tiles (15 different colors with the same color on diametrically opposite sides).
This is an internal view of a 3D sculpture by Anthony James. It is located in the Moco (Modern and Contemporary) Museum in Marble Arch, London.....The installation is a 60" Triacontahedron (Solar Black) 2024. Incase you were interested!
Thanks for visiting....
Model Rohombic Triacontahedron
Author Heinz Strobl
Paper 1,5x9-30 pieces, 1,5x6-60 pieces, 1x3-60 pieces.
Final size 7 cm.
Stellated rhombic triacontahedron
Designer: K.W.Hur
Parts: 30
Paper: 3.75*7.5cm(1:2)/traditional korean pattern paper
No glue
Rhombic triacontahedron, icosidodecahedron, cuboctahedron, and rhombic dodecahedron, all build with the hinges sideways
Let's go further through the Archimedean solids.
Here you see the compound of the icosidodecahedron and it's dual the rhombic triacontahedron.
Folder and designer of the modules: Dirk Eisner
240 units - 4 different modules
copy paper
last unit: 23.07.2014
30 units, designed by me. This origami model is heavily inspired by Stewart Coffin's eponymous wooden puzzle. Although it looks similar (same coloring and seams) it has a different internal structure. Upon closer study, its 6-coloring reveals some interesting properties. Crease pattern and some additional pictures can be found here.
The design represents one of the stellations of the Rhombic Triacontahedron. The small pictures show the 3- and 5-fold-axes.
There is also another recent origami rendition of this polyhedron, designed by Fergus Currie. For my version, I used Robert Webb's Stella: Polyhedron Navigator to get the accurate angles and distances. Folding all the modules took quite a long time and the assembly of the last units especially was a nightmare fun.
1. Great dodecicosidodecahedron, 2. Compound of dodecahedron and first stellation of icosahedron, 3. The return of the stellation with no name, 4. Compound of 5 dodecahedra, 5. 6 tetrahedra, 6. Compound of five cubes, 7. COmpound of five octahedra, 8. great ditrigonal icosidodecahedron, 9. Great Icosidodecahedron, 10. Compound of ten tetrahedra, 11. Dodecadodecahedron, 12. The 14th stellation of the icosahedron, 13. Compounds of tetrahedra, 14. Cuboctatruncated cuboctahedron, 15. great stellated dodecahedron, 16. Small ditrigonal icosidodecahedron, 17. Fourth stellation of the ditrigonal dodecadodecahedron, 18. Small icosicosidodecahedron, 19. Polyhedron models, 20. Polyhedron models, 21. Polyhedron models, 22. Third stellation of the icosahedron, 23. Fourth stellation of the icosahedron, 24. icosidodecadodecahedron, 25. Ditrigonal dodecadodecahedron, 26. Great icosihemidodecahedron, 27. Rhombic triacontahedron, 28. Pentagonal Hexecontahedron, 29. Tetrahemihexahedron, 30. Small cubicuboctahedron, 31. Truncated Great Icosahedron, 32. Octahemioctahedron, 33. Final Stellation of the cuboctahedron, 34. Rhombidodecadodecahedron, 35. Deltoidal hexecontahedron, 36. Sixth Stellation of the icosahedron
Created with fd's Flickr Toys
Explored!
a.k.a. Medial rhombic triacontahedron
60 units
Designer: Francesco Mancini
Folder: Francesco Mancini
Paper: Tinta unita by "Le mille gru"
Unit size: Square:
Diagram: BOS Convention book autumn 2012, QQM52
Reference: mathworld.wolfram.com/MedialRhombicTriacontahedron.html
Fifteen Interlocking Wrinkled Rhombic Prisms 180 units
In my hand.
This model has been on my list to design for years, so it is with great pleasure that I can finally call it complete. The original idea behind this was based on Daniel of 4 and 10 triangular prisms, and 6 pentagonal prisms, where the prismatic faces are not involved in the weaving of the model. Since the faces of a rhombic dodecahedron and triacontahedron are not rotated, the rotated must be forced by twisting the prisms in order to avoid key intersections. This works well near the top and bottom of the prism, where twisting maximizes distortion, but the closer you get towards the midpoint of prism edges, the less the distortion given by twisting. This is no problem for 6 rhombic prisms, based on a rhombic dodecahedron, where the intersections can be modelled, but the idea breaks down for 15 rhombic prisms, where the center intersections in the five fold axis's can't be practically modelled. Of course, the five-fold's here aren't exactly in the middle, but they are close enough that to make a non-wrinkled model where the only distortion is twisting would require paper proportions of at least 1:20, which also isn't practical. The wrinkles here not only dodge the intersections, but also take advantage of the naturally occurring convex bend of crimps to move the 5-fold axis's closer to the surface. I started a model on this premise about two years ago, but the proportional relationship between the faces and prism edges wasn't right so I put it aside, and only revived it again about two months ago.
This model is, as you would expect, challenging, but I didn't think it was that difficult. The version you see I wove a frame at a time without any frameholders.
I will upload a cheatsheet if anyone wants to try this. ;-)
Designed by me.
Folded out of Cordenons' Stardream paper.
Stellated rhombic triacontahedron
Designer: K.W.Hur
Parts: 30
Paper: 3.75*7.5cm(1:2)/traditional korean pattern paper
No glue
Ten Interlocking Irregular Hyperboloidal Triaugmented Omnitruncated Digonal Dihedra 150 units
2-fold view.
This, is, undoubtedly, the most time consuming project I have ever designed. I folded it three times in total to get the perfect proportions and angles, and combined with the design process, this took almost 40 hours to perfect. The compound is unique- it was a compound of ten irregular hexahedra before, but with the addition of thirty units which connect the frames, it has become something special. Tracing the connection between the frames is quite entertaining. I can only imagine at future presentations the number of people who will be scratching their heads trying to figure out what exactly is going on here. I'm not entirely sure myself. xD The exterior vertices roughly represent the vertices of a stellated rhombic triacontahedron...hmm.
Designed by me.
Folded out of Zanders' Elephant Hide paper.
Fifteen Interlocking Wrinkled Rhombic Prisms 180 units
5-fold view.
This model has been on my list to design for years, so it is with great pleasure that I can finally call it complete. The original idea behind this was based on Daniel of 4 and 10 triangular prisms, and 6 pentagonal prisms, where the prismatic faces are not involved in the weaving of the model. Since the faces of a rhombic dodecahedron and triacontahedron are not rotated, the rotated must be forced by twisting the prisms in order to avoid key intersections. This works well near the top and bottom of the prism, where twisting maximizes distortion, but the closer you get towards the midpoint of prism edges, the less the distortion given by twisting. This is no problem for 6 rhombic prisms, based on a rhombic dodecahedron, where the intersections can be modelled, but the idea breaks down for 15 rhombic prisms, where the center intersections in the five fold axis's can't be practically modelled. Of course, the five-fold's here aren't exactly in the middle, but they are close enough that to make a non-wrinkled model where the only distortion is twisting would require paper proportions of at least 1:20, which also isn't practical. The wrinkles here not only dodge the intersections, but also take advantage of the naturally occurring convex bend of crimps to move the 5-fold axis's closer to the surface. I started a model on this premise about two years ago, but the proportional relationship between the faces and prism edges wasn't right so I put it aside, and only revived it again about two months ago.
This model is, as you would expect, challenging, but I didn't think it was that difficult. The version you see I wove a frame at a time without any frameholders.
I will upload a cheatsheet if anyone wants to try this. ;-)
Designed by me.
Folded out of Cordenons' Stardream paper.
eine faszinierende Form. View Large On White
The Rhombic Icosahedron is a fascinating polyhedron.Thirty rhombic faces make up the surfaces. It is easy to fold the 30 modules, it looks like a little kusudama.
The name, having absolutely nothing to do with the geometry of the shape, was spontaneously thought of by a friend of mine (Shana Manion) who was making fun of the obscure names of the shapes I normally fold.
This model was folded from 60 1x6 rectangles and was inspired by the medial rhombic triacontahedron, although it really doesn't look much like that shape.
Diagrams here:
www.flickr.com/photos/8303956@N08/652338972/
Video tutorial here: www.youtube.com/watch?v=lQLCyAeXP6g
(Photography by Steven Toledo, a friend of mine)
This was actually what I had intended to make when I made the FIT + Black Hole model.
Folded from 60 1x7 proportioned rectangles (I hand-ripped them from standard 6" kami).
I like how the stars are actually framed in this model as opposed to the black hole model which covers them up.
Ten Interlocking Irregular Hyperboloidal Triaugmented Omnitruncated Digonal Dihedra 150 units
5-fold view.
This, is, undoubtedly, the most time consuming project I have ever designed. I folded it three times in total to get the perfect proportions and angles, and combined with the design process, this took almost 40 hours to perfect. The compound is unique- it was a compound of ten irregular hexahedra before, but with the addition of thirty units which connect the frames, it has become something special. Tracing the connection between the frames is quite entertaining. I can only imagine at future presentations the number of people who will be scratching their heads trying to figure out what exactly is going on here. I'm not entirely sure myself. xD The exterior vertices roughly represent the vertices of a stellated rhombic triacontahedron...hmm.
Designed by me.
Folded out of Zanders' Elephant Hide paper.
Here's a new model, made to make my OUSA convention table look less plain. Folded from 60 1x9 rectangles of kami.
Here it is in my hand as if I were summoning a ball of colorful energy xD
This model is to the Great Rhombic Triacontahedron as the Quadra-hadra-pudra-phedron is to the Medial Rhombic Triacontahedron. I've known for a long time that I "should" be able to make this model, but never got around to it.
Just like the Quadra-hadra-pudra-phedron, this model is made up of 12 5-piece woven-stars which are then woven into the final model. However, the dimensions and angles are all different.
I have named this model FIT + Black Hole because it looks kind of like an FIT (Five Intersecting Tetrahedra) whose edges are being sucked/stretched into a ball in the middle.
EDIT: It seems I am mistaken about the relationship between this and the QHPP... That was originally what I was trying to do, but it seems I have accidentally created this as an extra model by following a different assembly. What a fortunate accident! This is more closely related to an interpretation of the Great Stellated Dodecahedron, but it's not such a clear relationship.
The polyhedron sitting on top of my desk in this photo consists of 122 faces: 20 triangles, 60 squares, 30 golden rhombi (arranged as in the rhombic triacontahedron), and 12 pentagons. Constructed with b1s and r1s zome struts. It is a zonish form derived from the Icosidodecahedron expanded with six zones. George W. Hart discusses this and similar polyhedra on his page Zonish Polyhedra and on his book Zome Geometry.
According to Jim McNeill, the Expanded Rhombic Triacontahedron can also be produced from the Rhombic Triacontahedron by a process of expansion: "Each face of the Rhombic Triacontahedron is moved outwards until there is a distance of one unit between each originally adjacent face. These gaps are filled by the insertion of square faces. The remaining holes, corresponding to the original vertices of the Rhombic Triacontahedron can be filled by triangles and pentagons."
Video of this shape: www.youtube.com/watch?v=hjHI2c7LbAA
Made with 8754 Zen Magnets.
Another Interlaced Polyhedra construction - and man, was this one difficult! The two interlacing shapes are:
1) a stellated icosidodecahedron (with stellations on both the pentagonal and the triangular faces), and
2) a rhombic triacontahedron.
Credit for this construction goes to jasonbbb711 - he discovered the base shape (the icosidodecahedron), and it was his idea to stellate and interlace it.
Made with 3300 ZenMagnets.
This is a rhombic triacontahedron but it wasn't possible to make it completely stable...
Made with 8160 ZenMagnets
1 layer: rhombic triacontahedron
2 layer: dodecahedron
This would be easy to extend this but so far I don't have enough magnets... the next lvl needs 12960 magnets
Medial Rhombic Triacontahedron
Rhombic Hexecontahedron
After i have seen several renditions of these intriguing polyhedra I decided to create my own. Each one is folded from 60 units, standard golden rhombic units for the RH and kite-shaped versions from a square for the MRT. Interestingly, the ratio of its kite diagonals is also 1/φ but the shorter diagonal divides the longer one into two unequal segments, φ and 2-φ. Two kites actually form a big rhombus, partially hidden, with the diagonal ratio 1/φ^2.
Both polyhedra are stellations of the rhombic triacontahedron. The convex hull of the MRT is the icosahedron, connecting its innermost points creates a docecahedron, vice versa in case of the RH. Tracing the short diagonals of their faces, one can find an icosidodecahedron. Tracing the long diagonals gives a small stellated dodecahedron for the MRT and a great stellated dodecahedron for the RH. Amazing.
Resembling the geometry of a soccerball (truncated icosahedron), this shape is composed of pentagons and hexagons. Technically the pentagons of this model are indented. The hexagons are irregular based on the golden proportion (you can see this because there are corners where 3 hexagons meet, which would otherwise be flat if the hexagons were regular).
The model was folded from 30 squares.
Diagrams here:
www.flickr.com/photos/8303956@N08/652339064/
(Photography by Steven Toledo, a friend of mine)