- Source: Gyroelongated pentagonal cupola
In geometry, the gyroelongated pentagonal cupola is one of the Johnson solids (J24). As the name suggests, it can be constructed by gyroelongating a pentagonal cupola (J5) by attaching a decagonal antiprism to its base. It can also be seen as a gyroelongated pentagonal bicupola (J46) with one pentagonal cupola removed.
A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.
Area and Volume
With edge length a, the surface area is
A
=
1
4
(
20
+
25
3
+
(
10
+
5
)
5
+
2
5
)
a
2
≈
25.240003791...
a
2
,
{\displaystyle A={\frac {1}{4}}\left(20+25{\sqrt {3}}+\left(10+{\sqrt {5}}\right){\sqrt {5+2{\sqrt {5}}}}\right)a^{2}\approx 25.240003791...a^{2},}
and the volume is
V
=
(
5
6
+
2
3
5
+
5
6
2
650
+
290
5
−
2
5
−
2
)
a
3
≈
9.073333194...
a
3
.
{\displaystyle V=\left({\frac {5}{6}}+{\frac {2}{3}}{\sqrt {5}}+{\frac {5}{6}}{\sqrt {2{\sqrt {650+290{\sqrt {5}}}}-2{\sqrt {5}}-2}}\right)a^{3}\approx 9.073333194...a^{3}.}
Dual polyhedron
The dual of the gyroelongated pentagonal cupola has 25 faces: 10 kites, 5 rhombi, and 10 pentagons.
External links
Weisstein, Eric W., "Gyroelongated pentagonal cupola" ("Johnson solid") at MathWorld.
Kata Kunci Pencarian:
- Daftar bentuk matematika
- Gyroelongated pentagonal cupola
- Pentagonal cupola
- Gyroelongated triangular cupola
- Gyroelongated cupola
- Gyroelongated square cupola
- Johnson solid
- List of polygons, polyhedra and polytopes
- List of mathematical shapes
- Gyroelongated bicupola
- Icosahedron
