In
geometry, the pentagonal gyrobicupola is one of the
Johnson solid
In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that isohedral, each face must be the same polygon, or that the same polygons join around each Vertex (geometry), ver ...
s (). Like the
pentagonal orthobicupola (), it can be obtained by joining two
pentagonal cupola
In geometry, the pentagonal cupola is one of the Johnson solids (). It can be obtained as a slice of the rhombicosidodecahedron. The pentagonal cupola consists of 5 equilateral triangles, 5 squares, 1 pentagon, and 1 decagon.
Formulae
The fol ...
e () along their bases. The difference is that in this solid, the two halves are rotated 36 degrees with respect to one another.
The ''pentagonal gyrobicupola'' is the third in an infinite set of
gyrobicupolae.
The pentagonal gyrobicupola is what you get when you take a
rhombicosidodecahedron
In geometry, the rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces.
It has 20 regular triangular faces, 30 square (geometry), square face ...
, chop out the middle
parabidiminished rhombicosidodecahedron (), and paste the two opposing cupolae back together.
Formulae
The following
formula
In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informal use of the term ''formula'' in science refers to the general construct of a relationship betwee ...
e for
volume and
surface area
The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc ...
can be used if all
faces are
regular, with edge length ''a'':
[ Stephen Wolfram,]
Pentagonal gyrobicupola
from Wolfram Alpha
WolframAlpha ( ) is an answer engine developed by Wolfram Research. It answers factual queries by computing answers from externally sourced data.
WolframAlpha was released on May 18, 2009 and is based on Wolfram's earlier product Wolfram Mathe ...
. Retrieved July 24, 2010.
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References
External links
*
{{Polyhedron-stub
Johnson solids