In
geometry, the elongated pentagonal rotunda 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 (''J''
21). As the name suggests, it can be constructed by elongating a
pentagonal rotunda (''J''
6) by attaching a
decagonal prism to its base. It can also be seen as an
elongated pentagonal orthobirotunda
In geometry, the elongated pentagonal orthobirotunda is one of the Johnson solids (). Its Conway polyhedron notation iat5jP5 As the name suggests, it can be constructed by elongating a pentagonal orthobirotunda () by inserting a decagonal pri ...
(''J''
42) with one pentagonal rotunda removed.
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
The term regular can mean normal or in accordance with rules. It may refer to:
People
* Moses Regular (born 1971), America football player
Arts, entertainment, and media Music
* "Regular" (Badfinger song)
* Regular tunings of stringed instrum ...
, with edge length ''a'':
[ Stephen Wolfram,]
Elongated pentagonal rotunda
from Wolfram Alpha. Retrieved July 22, 2010.
Dual polyhedron
The dual of the elongated pentagonal rotunda has 30 faces: 10 isosceles triangles, 10 rhombi, and 10 quadrilaterals.
References
External links
*
{{Johnson solids navigator
Johnson solids