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Cupola (geometry)
*** Shopping-Tip: Cupola (geometry)
:''For other uses, see
cupola (disambiguation).''
{| border="1" bgcolor="#ffffff" cellpadding="5" align="right" style="margin-left:10px" width="250"
!bgcolor=#e7dcc3 colspan=2|Pentagonal cupola
|-
|align=center colspan=2|
Image:Pentagonal cupola.png 240px|Heptadecagonal antiprism
|-
|bgcolor=#e7dcc3|Type||Set of cupolas
|-
|bgcolor=#e7dcc3|Faces||n
triangles,
n
squares
1
polygon n-agon,
1 2n-agon
|-
|bgcolor=#e7dcc3|Edges||5n
|-
|bgcolor=#e7dcc3|Vertices||3n
|-
|bgcolor=#e7dcc3|
Symmetry group.html">Symmetry_group#Three_dimensions
''nv''.html" title="Meaning of |''C''''nv''
|-
|bgcolor=#e7dcc3|
Dual polyhedron||?
|-
|bgcolor=#e7dcc3|Properties||convex
|}
In
geometry, a '''cupola''' is a solid formed by joining two
polygons, one (the base) with twice as many edges as the other, by an alternating band of
triangles and
rectangles. The
triangular cupola triangular,
square cupola square, and
pentagonal cupola pentagonal cupolae all count among the
Johnson solids, and can be formed by taking sections of the
cuboctahedron,
rhombicuboctahedron, and
rhombicosidodecahedron, respectively.
A cupola can be seen as a
prism (geometry) prism where one of the polygons has been collapsed in half by merging alternate vertices.
Cupolae are a subclass of the
prismatoids.
Examples
{|
|-
|
Image:Geometric wedge.png thumb|left|128px|The [[wedge (geometry)|linear cupola (wedge)]]
|
Image:triangular_cupola.png thumb|left|128px|The [[triangular cupola with regular faces (J3)]]
|-
|
Image:square_cupola.png thumb|left|128px|The [[square cupola with regular faces (J4)]]
|
Image:Pentagonal cupola.png thumb|left|128px|The [[pentagonal cupola with regular faces (J5)]]
|}
Image:Tile3464bc.gif thumb|Plane "[[hexagonal cupolas" in one of
Tilings of regular polygons#Archimedean, uniform or semiregular tilings the 8 semiregular tessellations]]
The above-mentioned three polyhedra are the only non-trivial cupolae with regular faces: The "
hexagonal cupola" is a plane figure, and the
triangle triangular prism (geometry) prism might be considered a "cupola" of degree 2 (the cupola of a line segment and a square). However, cupolae of higher-degree polygons may be constructed with
Regular polygon#Taxonomic classification irregular triangular and rectangular faces.
Category:Polyhedra
Category:Prismatoid polyhedra
Category:Johnson solids
*** Shopping-Tip: Cupola (geometry)
