trapezohedron
Sign in to saveAlso known as antidipyramid, deltohedron, antibipyramid
In geometry, an trapezohedron, -trapezohedron, -antidipyramid, -antibipyramid, -deltohedron, or -antitegum, is the dual polyhedron of an antiprism. The faces of an are congruent and symmetrically staggered; they are called twisted kites. With a higher symmetry, its faces are kites (sometimes also called trapezoids, or deltoids). They are topologically related to the scalenohedra, which are half-symmetry variants with irregular trigons.
Key facts
- Polyhedron.name
- Set of dual-uniform trapezohedra
- Polyhedron.image
- Pentagonal trapezohedron.svg
- Polyhedron.caption
- Example: dual-uniform pentagonal trapezohedron ()
- Polyhedron.type
- dual-uniform in the sense of dual-semiregular polyhedron
- Polyhedron.faces
- congruent kites
- Polyhedron.schläfli
- {{math|{ } ⨁ {n}}}
- Polyhedron.symmetry
- order
- Polyhedron.rotation_group
- order
- Polyhedron.dual
- (convex) uniform antiprism
- Polyhedron.properties
- convex, face-transitive, regular vertices
via Wikipedia infobox
Wikidata facts
- Subclass of
- uniform polyhedron
- Image
- Octagonal trapezohedron.png
Show 6 more facts
- studied by
- solid geometry
- maintained by WikiProject
- WikiProject Mathematics
- has facet polytope
- kite
- dual to
- antiprism
- Commons category
- Trapezohedra
- different from
- deltahedron
Sources (1)
via Wikidata · CC0
~9 min read
Encyclopedic overview
8 sectionsContents
- Terminology
- Forms
- Special cases
- Symmetry
- Star trapezohedron
- See also
- References
- External links
{{Infobox polyhedron | name = Set of dual-uniform trapezohedra | image = Pentagonal trapezohedron.svg | caption = Example: dual-uniform pentagonal trapezohedron () | type = dual-uniform in the sense of dual-semiregular polyhedron | euler = | faces = congruent kites | edges = | vertices = | vertex_config = | schläfli = {{math|{ } ⨁ {n}}} | wythoff = | coxeter = | conway = | symmetry = order | rotation_group = order | surface_area = | volume = | dual = (convex) uniform antiprism | properties = convex, face-transitive, regular vertices | vertex_figure = | net = }}
In geometry, an trapezohedron, -trapezohedron, -antidipyramid, -antibipyramid, -deltohedron, or -antitegum, is the dual polyhedron of an antiprism. The faces of an are congruent and symmetrically staggered; they are called twisted kites. With a higher symmetry, its faces are kites (sometimes also called trapezoids, or deltoids). They are topologically related to the scalenohedra, which are half-symmetry variants with irregular trigons.
Excerpted from Wikipedia’s “trapezohedron” article, available under the CC BY-SA 4.0 licence.