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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.
Medial rhombic triacontahedron; Hexahemioctacron; Hemipolyhedron; Octahemioctacron; ... Table of Shapes Section Sub-Section Sup-Section Name Algebraic Curves ¿ Curves
Toggle the table of contents. Table of polyhedron dihedral angles. 1 language. Slovenščina; ... Rhombic triacontahedron (Dual of icosidodecahedron) — V(3.5.3.5)
Alternatively, if you expand each of five cubes by moving the faces away from the origin the right amount and rotating each of the five 72° around so they are equidistant from each other, without changing the orientation or size of the faces, and patch the pentagonal and triangular holes in the result, you get a rhombicosidodecahedron ...
Rhombic triacontahedron V(3.5) 2 Johannes Kepler coined the category semiregular in his book Harmonices Mundi (1619), including the 13 Archimedean solids , two infinite families ( prisms and antiprisms on regular bases), and two edge-transitive Catalan solids , the rhombic dodecahedron and rhombic triacontahedron .
rhombic triacontahedron: 30 rhombi: 60 32 144° I h: triakis icosahedron: 60 isosceles triangles 90 32 160.613° I h: pentakis dodecahedron: 60 isosceles triangles 90 32 156.719° I h: deltoidal hexecontahedron: 60 kites 120 62 154.121° I h: disdyakis triacontahedron: 120 scalene triangles 180 62 164.888° I h: pentagonal hexecontahedron: 60 ...
In geometry, the great rhombic triacontahedron is a nonconvex isohedral, isotoxal polyhedron. It is the dual of the great icosidodecahedron (U54). Like the convex rhombic triacontahedron it has 30 rhombic faces, 60 edges and 32 vertices (also 20 on 3-fold and 12 on 5-fold axes).
For example a tetrahedron is a polyhedron with four faces, a pentahedron is a polyhedron with five faces, a hexahedron is a polyhedron with six faces, etc. [29] For a complete list of the Greek numeral prefixes see Numeral prefix § Table of number prefixes in English, in the column for Greek cardinal numbers.