Rhombic triacontahedron template

Just try it. I hope this helps clarify the original instruction, which were lacking on the most important step. Reply 14 years ago on Introduction. Your second shape is a rhombic dodecahedron; it's easier with a different size sheet of paper. I started out with the bottom half of this page and then figured out this shape; just the opposite of you.

Your first shape doesn't have a specific name it's a kind of penrose tiling. You photographed this instructable 2 years in advance! Great to be prepared! What exactly is it and why?

Reply 15 years ago. I got a two year old camera for Christmas - that's preparation in my family ; - and I thought I'd try it out with an instructable. It shows up a lot in geometry so it gets its own name. The rhombi should be 1. The easiest way to do that is with a "continued fraction approximation. Some of us had HS geometry in the early 70's and don't have quite that good of recall.

It's interesting to be reminded of it periodically. Introduction: Rhombic Triacontahedron. Did you make this project? Share it with us! The compound of five cubes that forms a dodecahedron is discussed below. Chamfering a cube is the same as cantellation. The edges are truncated instead of the corners being truncated. The cube transforms into the dodecahedron if the edges of the cube are pushed into planes. The compound of five cubes is composed of 5 cubes as its name suggests. It is dual to the compound of five octahedra.

The Icosahedron and dodecahedron are duals. Connecting the centers of the faces creates the dual. Purusha is the anthropocosmic, paradigmatic Man or Seed that projects Prakriti, the eternally enchanting Feminine, in order that her womb may give birth to his own embodiment in the world of form.

The Hindu tradition associates the icosahedron with Purusha — the seed-image of Brahma, the supreme creator. Purusha is envisioned as unmanifest and untouched by creation — just as in the following drawings, the icosahedron is untouched by the other forms. All other volumes arise naturally out of the icosahedron, making it one obvious choice for the first form. Within this womb of creation, all shapes and forms are present in potentiation.

The star born within its pentagon is the configuration of Cosmic Man, the perfecter of life, the Golden Proportion. Both Prakriti dodecahedron and Purusha icosahedron have phi proportions.

The whole coagulation is begun by the secret seed which contracts the circle, the infinite, undifferentiated spirit, into the icosahedron. The seed is phi, the fire of spirit. The golden spiral is shown in black.

The sequence of root 2 ratios is shown in red. The star tetrahedron, or stellated octahedron, is seen as the yin and the yang due to its upward pointing tetrahedron and downward pointing tetrahedron.

The tetrahedron is a volume of threeness — a primary symbol of function accompanied by its reciprocal. Recall that there is an octahedron at the center of the star tetrahedron. The octahedron symbolizes the crystallization, the static perfection of matter. It is the transformed and clarified lens of light — the double pyramid. The result of the harmonic interaction of the star tetrahedron gives birth to the cube. The triakis icosahedron is the dual of the truncated dodecahedron.

It is a Catalan solid. The triakis icosahedron is a Kleetope of the icosahedron. This means that it is an icosahedron with triangular pyramids added to each face. The Snub Dodecahedron is an Archimedean solid that has two distinct forms that are mirror images enantiomorphs of one another. The Snub Dodecahedron has the highest sphericity 0. At a proper distance this can create the rhombicosidodecahedron by filling in square faces between the divided edges and triangle faces between the divided vertices.

But for the snub form, only add the triangle faces and leave the square gaps empty. Then apply an equal rotation to the centers of the pentagons and triangles, continuing the rotation until the gaps can be filled by two equilateral triangles. Here is the transition from the rhombicosidodecahedron to the snub dodecahedron:.

The Pentagonal Hexecontahedron is the dual of the Snub Dodecahedron. Like the snub dodecahedron, there are two mirror image forms enantiomorphs. The Pentagonal Hexecontahedron can be constructed by adding pentagonal pyramids to the 12 pentagonal faces of the snub dodecahedron, then adding triangular pyramids to the 20 triangular faces that do not share an edge with a pentagon.

The Icosidodecahedron is an Archimedean solid that combines the 12 pentagonal faces of the dodecahedron with the 20 triangular faces of the icosahedron. Its edges form 6 equatorial decagons that give a radial projection of 6 great circles.

The icosidodecahedron is the rectification of both the dodecahedron and icosahedron. It is the full-edge truncation between both of these solids, just as the cuboctahedron is between the octahedron and the cube. The ratio of the long diagonal to the short diagonal of each face equals the golden ratio.

Thus the face is called a golden rhombus. It contains ten tetrahedra, five cubes, an icosahedron and a dodecahedron. The centers of the faces contain five octahedra. The cube can transform into a rhombic triacontahedron by dividing its square faces into 4 squares and splitting middle edges into new rhombic faces. This is seen below:. The truncated icosidodecahedron is also known as the Great Rhombicosidodecahedron.

It is an Archimedean solid. If one truncates an icosidodecahedron by cutting the corners off, one does not get this uniform figure: instead of squares the truncation has golden rectangles. The Disdyakis Triacontahedron is the dual of the truncated icosidodecahedron.

Projected onto a sphere, the disdyakis triacontahedron forms 15 great circles. This is the same spherical projection as the compound of five octahedra. The Rhombicosidodecahedron is also called the small rhombicosidodecahedron. It works best if the class is divided into groups of four to eight students. Each group works to make one puzzle.

The paper clips are handy for accessing the interior of the blocks when applying tape. Other thin, rigid objects can work as well. We find that a light color of paper looks best as the tape is less obvious.