Pentahedron: Difference between revisions
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{{for|the Sylvester pentahedron of a cubic surface|quaternary cubic}} | {{for|the Sylvester pentahedron of a cubic surface|quaternary cubic}} | ||
In [[geometry]], a '''pentahedron''' ({{plural form}}: '''pentahedra''') is a [[polyhedron]] with five faces or sides. There are no [[face-transitive]] polyhedra with five sides and there are two distinct topological types. | In [[geometry]], a '''pentahedron''' ({{plural form}}: '''pentahedra''') is a [[polyhedron]] with five faces or sides. There are no [[face-transitive]] polyhedra with five sides, and there are two distinct topological types. Notable polyhedra with [[regular polygon]] faces are: | ||
<gallery widths="180" heights="180"> | |||
File:Square pyramid.png|[[Square pyramid]] with four triangles and one square.{{r|berman}} Pyramids with any quadrilateral base have the same number of faces. | |||
File:Triangular prism.png|[[Triangular prism]] with three rectangles and two triangular bases.{{r|berman}} In the case of a right triangular prism, it is a special case of [[wedge (geometry)]] with connecting parallel edges between triangles; the wedge generally has two triangles and three quadrilateral faces.{{r|haul}} | |||
File:截一角正四面體.gif | |||
</gallery> | |||
== Concave == | |||
An irregular pentahedron can be a non-[[Convex polytope|convex]] solid: Consider a non-convex (planar) [[quadrilateral]] (such as a [[dart (geometry)|dart]]) as the base of the solid, and any point not in the base plane as the [[apex (geometry)|apex]]. | |||
==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 [[hosohedron|pentagonal hosohedron]] with [[Schläfli symbol]] {2,5}. It has 2 ([[antipodal point]]) vertices, 5 edges, and 5 digonal faces. | |||
==References== | |||
{{Reflist|refs= | |||
<ref name="berman">{{cite journal | |||
| last = Berman | first = Martin | | last = Berman | first = Martin | ||
| year = 1971 | | year = 1971 | ||
| Line 15: | Line 31: | ||
}}</ref> | }}</ref> | ||
< | <ref name="haul">{{cite book | ||
| last = Haul | first = Wm. S. | |||
| year = 1893 | |||
| title = Mensuration | |||
| url = https://archive.org/details/mensuration00hallgoog/page/n57/mode/1up?view=theater&q=wedge | |||
| page = 45 | |||
| publisher = Ginn & Company | |||
}}</ref> | |||
}} | |||
==External links== | ==External links== | ||
Latest revision as of 16:04, 27 June 2025
Template:Expand Chinese Template:Short description Template:More sources needed Script error: No such module "For". In geometry, a pentahedron (Template:Plural form: pentahedra) is a polyhedron with five faces or sides. There are no face-transitive polyhedra with five sides, and there are two distinct topological types. Notable polyhedra with regular polygon faces are:
-
Square pyramid with four triangles and one square.Template:R Pyramids with any quadrilateral base have the same number of faces.
-
Triangular prism with three rectangles and two triangular bases.Template:R In the case of a right triangular prism, it is a special case of wedge (geometry) with connecting parallel edges between triangles; the wedge generally has two triangles and three quadrilateral faces.Template:R
Concave
An irregular pentahedron can be a non-convex solid: Consider a non-convex (planar) quadrilateral (such as a dart) as the base of the solid, and any point not in the base plane as the apex.
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.
References
External links
- Script error: No such module "Template wrapper".