- Source: Elongated pentagonal pyramid
In geometry, the elongated pentagonal pyramid is one of the Johnson solids (J9). As the name suggests, it can be constructed by elongating a pentagonal pyramid (J2) by attaching a pentagonal prism to its base.
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.
Formulae
The following formulae for the height (
H
{\displaystyle H}
), surface area (
A
{\displaystyle A}
) and volume (
V
{\displaystyle V}
) can be used if all faces are regular, with edge length
L
{\displaystyle L}
:
H
=
L
⋅
(
1
+
5
−
5
10
)
≈
L
⋅
1.525731112
{\displaystyle H=L\cdot \left(1+{\sqrt {\frac {5-{\sqrt {5}}}{10}}}\right)\approx L\cdot 1.525731112}
A
=
L
2
⋅
20
+
5
3
+
25
+
10
5
4
≈
L
2
⋅
8.88554091
{\displaystyle A=L^{2}\cdot {\frac {20+5{\sqrt {3}}+{\sqrt {25+10{\sqrt {5}}}}}{4}}\approx L^{2}\cdot 8.88554091}
V
=
L
3
⋅
(
5
+
5
+
6
25
+
10
5
24
)
≈
L
3
⋅
2.021980233
{\displaystyle V=L^{3}\cdot \left({\frac {5+{\sqrt {5}}+6{\sqrt {25+10{\sqrt {5}}}}}{24}}\right)\approx L^{3}\cdot 2.021980233}
Dual polyhedron
The dual of the elongated pentagonal pyramid has 11 faces: 5 triangular, 1 pentagonal and 5 trapezoidal. It is topologically identical to the Johnson solid.
See also
Elongated pentagonal bipyramid
References
External links
Weisstein, Eric W., "Johnson solid" ("Elongated pentagonal pyramid") at MathWorld.
Kata Kunci Pencarian:
- Daftar bentuk matematika
- Elongated pentagonal pyramid
- Pentagonal pyramid
- Elongated pentagonal bipyramid
- Johnson solid
- Elongated pyramid
- List of mathematical shapes
- List of polygons, polyhedra and polytopes
- Hendecahedron
- J9
- Dodecahedron
