Pentahedron

Pentahedron

In geometry, a pentahedron (plural: pentahedra) is a polyhedron with five faces. Since there are no face-transitive polyhedra with five sides and there are two distinct topological types, this term is rarely used.

With regular polygon faces, the two topological forms types are the square pyramid and triangular prism. Geometric variations with irregular faces can also be constructed.

The "square pyramid" can be seen as a degenerate "triangular prism" where one edge of its side edges is collapsed into a point, losing one edge and one vertex, and changing two squares into triangles.

Hosohedron

There is a third topological polyhedral figure with 5 faces, degenerate as a polyhedron, it exists as a spherical tiling of digon faces, called a pentagonal hosohedron with Schläfli symbol {2,5}. It has 2 (antipodal point) vertices, 5 edges, and 5 digonal faces.

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Look at other dictionaries:

  • Pentahedron — Pen ta*he dron, n. [Penta + Gr. e dra seat, base.] A solid figure having five sides. [1913 Webster] …   The Collaborative International Dictionary of English

  • pentahedron — [pen΄tə hē′drən] n. pl. pentahedrons or pentahedra [pen΄tə hē′drə] [ModL: see PENTA & HEDRON] a solid figure with five plane surfaces pentahedral adj …   English World dictionary

  • pentahedron — noun Etymology: New Latin Date: circa 1775 a solid bounded by five faces • pentahedral adjective …   New Collegiate Dictionary

  • pentahedron — pentahedral, adj. /pen teuh hee dreuhn/, n., pl. pentahedrons, pentahedra / dreuh/. a solid figure having five faces. [1655 65; PENTA + HEDRON] * * * …   Universalium

  • pentahedron — noun A solid geometric figure with five faces …   Wiktionary

  • pentahedron — pen·ta·he·dron || ‚pentÉ™ hɪːdrÉ‘n , he / drÉ‘n n. solid figure having five faces …   English contemporary dictionary

  • pentahedron — [ˌpɛntə hi:dr(ə)n, hɛd ] noun (plural pentahedra drə or pentahedrons) a solid figure with five plane faces. Derivatives pentahedral adjective …   English new terms dictionary

  • pentahedron — pen·ta·he·dron …   English syllables

  • pentahedron — pen•ta•he•dron [[t]ˌpɛn təˈhi drən[/t]] n. pl. drons, dra ( drə). math. a solid figure having five faces …   From formal English to slang

  • pentahedron — /pɛntəˈhidrən/ (say pentuh heedruhn) noun (plural pentahedrons or pentahedra /pɛntəˈhidrə/ (say pentuh heedruh)) a solid figure having five faces. –pentahedral, adjective …  

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