Icosahedron

The icosahedron is one of the five Platonic solids. It contains 20 triangles joined five to a vertex. It can also be considered as a snubbed tetrahedron. Coordinates The coordinates of an icosahedron with edge length 2 are: (0, ±1, ±φ) (±1, ±φ, 0) (±φ, 0, ±1)

Wikizero

1.1 Convex regular icosahedron 1.2 Great icosahedron 2 Stellated icosahedra 3 Pyritohedral symmetry 3.1 Cartesian coordinates 3.2 Jessen’s icosahedron 4 Other icosahedra 4.1 Rhombic icosahedron 4.2 Pyramid and prism symmetries 4.3 Johnson solids 5 6

Icosahedron

An icosahedron is a three-dimensional regular polyhedron with 20 faces, each of which is triangular. There are five faces to each vertex. It is called a hydrohedron under the elemental system, and its Bowers name is ike. 1 Symbols 2 Structure and Subfacets 2.1 Hypervolumes 2.2 Subfacets 2.3 Radii 2.4 Angles 2.5 Vertex coordinates 2.6 Related shapes 3 See also Dynkin based symbols of the

Icosahedron

1.1 Convex regular icosahedron 1.2 Great icosahedron 2 Stellated icosahedra 3 Pyritohedral symmetry 3.1 Cartesian coordinates 3.2 Jessen’s icosahedron 4 Other icosahedra 4.1 Rhombic icosahedron 4.2 Pyramid and prism symmetries 4.3 Johnson solids 5 6

Regular icosahedron

Template:Reg polyhedron stat table File:Regular icosahedron.stl In geometry, a regular icosahedron (/ ˌ aɪ k ɒ s ə ˈ h iː d r ən,-k ə-,-k oʊ-/ or / aɪ ˌ k ɒ s ə ˈ h iː d r ən /) is a convex polyhedron with 20 faces, 30 edges and 12 vertices. It is one of the five , and the

## Don Zagier The icosahedron, the Rogers- Ramanujan identites, …

· PDF 檔案Icosahedron 12 30 20 Point Coordinates in Coordinates in 0 The icosahedron looks as follows: The coordinates of the vertices are (a nice exercise!) where and , and I am using stereographic projection to map to via 2. Finite groups Let be the icosahedral

Truncated icosahedron

In geometry, the truncated icosahedron is an Archimedean solid, one of 13 convex isogonal nonprismatic solids whose 32 faces are two or more types of regular polygons.It is the only one of these shapes that does not contain triangles or squares. It has 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges.

Construction ·

## Cartesian coordinates

Cartesian coordinates Let ϕ {\displaystyle \phi } be the golden ratio . The 12 points given by ( 0 , ± 1 , ± ϕ ) {\displaystyle (0,\pm 1,\pm \phi )} and cyclic permutations of these coordinates are the vertices of a regular icosahedron .

## truncated icosahedron coordinates to build a dome : …

To build a bamboo geodesic dome The spans from joint to joint are BB, BR, or RR. The arc factors of these lengths are: BB=.26030616, BR=.31030984, RR=.32636688. For these factors, the radius of the dome is 1.00. To construct a 22′ dome (11′ radius) the

## Coordinates of the vertices of polyhedra

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Truncated Icosahedron

Truncated Icosahedron Calculator Calculations at a regular truncated icosahedron. A truncated icosahedron is constructed by cutting off the vertices of an icosahedron in a way, so that every edge has the same length. This solid is famous as soccer ball shape and

Spinning Icosahedron

It is called an icosahedron because it is a polyhedron that has 20 faces (from Greek icosa-meaning 20) When we have more than one icosahedron they are called icosahedra When we say “icosahedron” we often mean “regular icosahedron” (in other words all faces are the same size and shape), but it doesn’t have to be – this is also an icosahedron, even though all faces are not the same.

## Ikosaeder – Wikipedia

Das (auch, v. a. österr.: der) Ikosaeder [ikozaˈʔeːdɐ] (von altgriechisch εἰκοσάεδρον eikosáedron „Zwanzigflach“, „Zwanzigflächner“)[1] ist einer der fünf platonischen Körper, genauer ein regelmäßiges Polyeder (Vielflach, Vielflächner) mit 20 kongruenten gleichseitigen Dreiecken als Seitenflächen 30 …

Symmetrie ·

rendering

Create an icosahedron and recursively subdivide faces until desired tessellation reached. Sphere using spherical coordinates walk For the first way, you just use a double nested for to walk theta and phi.

## PDB-101: Learn: Guide to Understanding PDB Data: …

The deposited coordinates represent 1 icosahedral asymmetric unit. This unit is represented by ribbons in all views. The crystal asymmetric unit is pentameric. The biological assembly is an icosahedron (as show above). The complete crystal unit cell contains 2

## Icosahedron3D

Icosahedron3D class captures information defining a Icosahedron instantiation with specified: – xyz location of the Icosahedron center (user coordinate scale) – size (user coordinate scale), edge-length is 2*size – xyz rotations (optional) – PhongMaterial (optional