Heptahedron


Heptahedron

A heptahedron (plural: heptahedra) is a polyhedron having seven sides, or faces.

A heptahedron can take a surprising number of different basic forms, or topologies. Probably most familiar are the hexagonal pyramid and the pentagonal prism. Also notable is the Tetrahemihexahedron, whose seven equilateral triangle faces form a rudimentary projective plane.

Topologically distinct heptahedra

Convex

There are 34 topologically distinct "convex" heptahedra, excluding mirror images. [ [http://home.att.net/~numericana/data/polycount.htm Counting polyhedra] ] (Two polyhedra are "topologically distinct" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.)

An example of each type is depicted below, along with the number of sides on each of the faces. The images are ordered by descending number of six-sided faces (if any), followed by descending number of five-sided faces (if any), and so on.

Concave

References

External links

* [http://www.uwgb.edu/dutchs/symmetry/poly4-7f.htm Polyhedra with 4-7 Faces] by Steven Dutch


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Look at other dictionaries:

  • Heptahedron — Hep ta*he dron, n. [Hepta + Gr. ? seat, base, fr. ? to sit: cf. F. hepta[ e]dre.] (Geom.) A solid figure with seven sides. [1913 Webster] …   The Collaborative International Dictionary of English

  • heptahedron — [hep΄tə hē′drən] n. pl. heptahedrons or heptahedra [hep΄tə hē′drə] [ModL: see HEPTA & HEDRON] a solid figure with seven plane surfaces heptahedral adj …   English World dictionary

  • heptahedron — heptahedral, heptahedrical, adj. /hep teuh hee dreuhn/, n., pl. heptahedrons, heptahedra / dreuh/. a solid figure having seven faces. [1650 60; HEPTA + HEDRON] * * * …   Universalium

  • heptahedron — noun any polyhedron having seven faces …   Wiktionary

  • heptahedron —    A polyhedron having seven polygonal faces. The plural can be either heptahedrons or heptahedra. Also see mathematics and vertex …   Glossary of Art Terms

  • heptahedron — [ˌhɛptə hi:drən, hɛd ] noun (plural heptahedra or heptahedrons) a solid figure with seven plane faces. Derivatives heptahedral adjective …   English new terms dictionary

  • heptahedron — /hɛptəˈhidrən/ (say heptuh heedruhn) noun (plural heptahedrons or heptahedra /hɛptəˈhidrə/ (say heptuh heedruh)) a solid figure having seven faces. –heptahedral, adjective …   Australian English dictionary

  • heptahedron —   n. seven sided solid figure.    ♦ heptahedral, a …   Dictionary of difficult words

  • heptahedron — n. a solid figure with seven faces. Derivatives: heptahedral adj. Etymology: HEPTA + HEDRON after POLYHEDRON …   Useful english dictionary

  • Polyhedron — Polyhedra redirects here. For the relational database system, see Polyhedra DBMS. For the game magazine, see Polyhedron (magazine). For the scientific journal, see Polyhedron (journal). Some Polyhedra Dodecahedron (Regular polyhedron) …   Wikipedia


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