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Pentagonal gyrobicupola

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Pentagonal gyrobicupola
TypeBicupola,
Johnson
J30J31J32
Faces10 triangles
10 squares
2 pentagons
Edges40
Vertices20
Vertex configuration
Symmetry group
Propertiesconvex, composite
Net

The pentagonal gyrobicupola is a polyhedron that is constructed by attaching two pentagonal cupolas base-to-base, each of its cupolas is twisted at 36°. It is an example of a Johnson solid and a composite polyhedron.

Construction

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The pentagonal gyrobicupola is a composite polyhedron: it is constructed by attaching two pentagonal cupolas base-to-base. This construction is similar to the pentagonal orthobicupola; the difference is that one of cupolas in the pentagonal gyrobicupola is twisted at 36°, as suggested by the prefix gyro-. The resulting polyhedron has the same faces as the pentagonal orthobicupola does: those cupolas cover their decagonal bases, replacing it with eight equilateral triangles, eight squares, and two regular pentagons.[1] A convex polyhedron in which all of its faces are regular polygons is the Johnson solid. The pentagonal gyrobicupola has such these, enumerating it as the thirty-first Johnson solid .[2]

Properties

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Because it has a similar construction as the pentagonal orthobicupola, the surface area of a pentagonal gyrobicupola is the sum of polygonal faces' area, and its volume is twice the volume of a pentagonal cupola for which slicing it into those:[1]

References

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  1. ^ a b Berman, Martin (1971). "Regular-faced convex polyhedra". Journal of the Franklin Institute. 291 (5): 329–352. doi:10.1016/0016-0032(71)90071-8. MR 0290245.
  2. ^ Francis, Darryl (August 2013). "Johnson solids & their acronyms". Word Ways. 46 (3): 177.
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