In
geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
, the pentagonal gyrocupolarotunda is one of the
Johnson solid
In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons. They are sometimes defined to exclude the uniform polyhedrons. There are ninety-two Solid geometry, s ...
s (). Like the
pentagonal orthocupolarotunda
In geometry, the pentagonal orthocupolarotunda is one of the Johnson solids (). As the name suggests, it can be constructed by joining a pentagonal cupola () and a pentagonal rotunda () along their decagonal bases, matching the pentagonal face ...
(), it can be constructed by joining a
pentagonal cupola
Properties
The pentagonal cupola (geometry), cupola's faces are five equilateral triangles, five squares, one regular pentagon, and one regular decagon. It has the property of Convex set, convexity and regular polygonal faces, from which it is ...
() and a
pentagonal rotunda
The pentagonal rotunda is a convex polyhedron with regular polygonal faces. These faces comprise ten equilateral triangles, six regular pentagons, and one regular decagon, making a total of seventeen. The pentagonal rotunda is an example of Johns ...
() along their
decagon
In geometry, a decagon (from the Greek δέκα ''déka'' and γωνία ''gonía,'' "ten angles") is a ten-sided polygon or 10-gon.. The total sum of the interior angles of a simple decagon is 1440°. Regular decagon
A '' regular decagon'' has a ...
al bases. The difference is that in this solid, the two halves are rotated 36 degrees with respect to one another.
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 betwe ...
e for
volume
Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch) ...
and
surface area
The surface area (symbol ''A'') 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 d ...
can be used if all
faces
The face is the front of the head that features the eyes, nose and mouth, and through which animals express many of their emotions. The face is crucial for human identity, and damage such as scarring or developmental deformities may affect the ...
are
regular
Regular may refer to:
Arts, entertainment, and media Music
* "Regular" (Badfinger song)
* Regular tunings of stringed instruments, tunings with equal intervals between the paired notes of successive open strings
Other uses
* Regular character, ...
, with edge length ''a'':
Stephen Wolfram
Stephen Wolfram ( ; born 29 August 1959) is a British-American computer scientist, physicist, and businessman. He is known for his work in computer algebra and theoretical physics. In 2012, he was named a fellow of the American Mathematical So ...
,
Pentagonal gyrocupolarotunda
from Wolfram Alpha
WolframAlpha ( ) is an answer engine developed by Wolfram Research. It is offered as an online service that answers factual queries by computing answers from externally sourced data.
History
Launch preparations for WolframAlpha began on Ma ...
. Retrieved July 24, 2010.
:
:
References
External links
*
Johnson solids
{{Polyhedron-stub