query: has_facet_polytope dodecahedron
supports: In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent regular polygonal faces with the same number of faces meeting at each vertex. Five solids meet those criteria: In geometry, a face diagonal of a polyhedron is a diagonal on one of the faces, in contrast to a space diagonal passing through the interior of the polyhedron. In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be convex or star. In the limit, a sequence of regular polygons with an increasing number of sides becomes a circle, if the perimeter is fixed, or a regular apeirogon, if the edge length is fixed. A regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular composed of twelve regular pentagonal faces, with three meeting at each vertex, and is represented by the Schläfli symbol {5,3}. It is one of the five Platonic solids. It has 12 faces, 20 vertices, 30 edges, and 160 diagonals (60 face diagonals, 100 space diagonals). In geometry , a dodecahedron ( Greek  , from  ddeka `` twelve '' +  hédra `` base '' , `` seat '' or `` face '' ) is any polyhedron with twelve flat faces . The most familiar dodecahedron is the regular dodecahedron , which is a Platonic solid . There are also three regular star dodecahedra , which are constructed as stellations of the convex form . All of these have icosahedral symmetry , order 120 . The pyritohedron is an irregular pentagonal dodecahedron , having the same topology as the regular one but pyritohedral symmetry while the tetartoid has tetrahedral symmetry . The rhombic dodecahedron , seen as a limiting case of the pyritohedron has octahedral symmetry . The elongated dodecahedron and trapezo - rhombic dodecahedron variations , along with the rhombic dodecahedra are space - filling . There are a large number of other dodecahedra . In elementary geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices. The word polyhedron comes from the Classical Greek , as "poly-" (stem of , "many") + "-hedron" (form of , "base" or "seat"). In geometry, a pentagon (from the Greek  "pente" and  "gonia", meaning "five" and "angle") is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°. The Multinational Aircrew Electronic Warfare Tactics Facility Polygone - POLYGON is an Electronic Warfare Tactics Range located on the border between Germany and France. It is a tri-national facility operated by France, Germany and the United States. A regular icosahedron has 60 rotational (or orientation-preserving) symmetries, and a symmetry order of 120 including transformations that combine a reflection and a rotation. A regular dodecahedron has the same set of symmetries, since it is the dual of the icosahedron. In geometry a space diagonal (also interior diagonal, body diagonal or triagonal) of a polyhedron is a line connecting two vertices that are not on the same face. Space diagonals contrast with face diagonals, which connect vertices on the same face (but not on the same edge) as each other.
candidates: face pentagon polygon regular dodecahedron vertex
answer: polygon