page_title: Rhombic triacontahedron
section_title: Uses
hierarchical_section_title: Rhombic triacontahedron / Uses
caption_attribution_description: English: IQ-light. Design by Holger Strøm. Original rhombic triacontahedron-shape.
context_page_description: In geometry, the rhombic triacontahedron, sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces. It has 60 edges and 32 vertices of two types. It is a Catalan solid, and the dual polyhedron of the icosidodecahedron. It is a zonohedron.
  The ratio of the long diagonal to the short diagonal of each face is exactly equal to the golden ratio, φ, so that the acute angles on each face measure 2 tan⁻¹ = tan⁻¹, or approximately 63.43°. A rhombus so obtained is called a golden rhombus.
  Being the dual of an Archimedean solid, the rhombic triacontahedron is face-transitive, meaning the symmetry group of the solid acts transitively on the set of faces. This means that for any two faces, A and B, there is a rotation or reflection of the solid that leaves it occupying the same region of space while moving face A to face B.
  The rhombic triacontahedron is somewhat special in being one of the nine edge-transitive convex polyhedra, the others being the five Platonic solids, the cuboctahedron, the icosidodecahedron, and the rhombic dodecahedron.
context_section_description: Danish designer Holger Strøm used the rhombic triacontahedron as a basis for the design of his buildable lamp IQ-light (IQ for "Interlocking Quadrilaterals").
  Woodworker Jane Kostick builds boxes in the shape of a rhombic triacontahedron. The simple construction is based on the less than obvious relationship between the rhombic triacontahedron and the cube.
  Roger von Oech's "Ball of Whacks" comes in the shape of a rhombic triacontahedron.
  The rhombic triacontahedron is used as the "d30" thirty-sided die, sometimes useful in some roleplaying games or other places.
  Christopher Bird, co-author of The Secret Life of Plants wrote an article for New Age Journal in May, 1975, popularizing the dual icosahedron and dodecahedron as "the crystalline structure of the Earth," a model of the "Earth (telluric) energy Grid." The EarthStar Globe by Bill Becker and Bethe A. Hagens purports to show "the natural geometry of the Earth, and the geometric relationship between sacred places such as the Great Pyramid, the Bermuda Triangle, and Easter Island." It is printed as a rhombic triacontahedron, on 30 diamonds, and folds up into a globe.
caption: An example of the use of a rhombic triacontahedron in the design of a lamp
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