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written by Rene K. Mueller, Copyright (c) 2007, last updated Wed, January 9, 2008
Square Pyramid 
 Johnson Solid: J1
 Vertices: 5
 Faces: 5
 Edges: 8
 V: s^{3} / 6 * √2
 A: s^{2} * (1 + √3)

General Pyramid 
The general pyramid:
 q = √((s/2)^{2} + h^{2})
 l = √((s/2)^{2} + q^{2})
 A = 2 s q + s^{2}
 A_{wall/roof} = 2 s q
 V = s^{2} h / 3
Most obvious association with pyramids comes from the egyptian pyramids in Giza and those of the mayans in south america.
It is also apparent those pyramids have been built with enormous effort and skills which is now honored by the durability of thousands of years.
The largest pyramid in Giza is the Khufu Pyramid, with following values:
 s = 231m (original) (now: 230.4m)
 h = 146.6m (original) (now: 138.8m)
thereby
 q = 186.632m
 l = 219.478m
Interesting ratio:
 s/h = 1.57571.. ~ π/2 ~ 11/7
Read more at Great Pyramid of Giza .
Pentagonal Pyramid 
 Johnson Solid: J2
 Vertices: 6
 Faces: 6
 Edges: 10
 V: s^{3} / 24 * (5 + √5)
 A: s^{2} / 2 * √(5/2 * (10 + √10 + √(75+30*√5))

The roof isn't very steep, unless those roof struts would be made longer  it would be a very simplistic habitat.
Triangular Cupola 
 Johnson Solid: J3
 Vertices: 9
 Faces: 8
 Edges: 15
 V: s^{3} * (5/(5*√2))
 A: s^{2} * (3+5/2*√3)

Square Cupola 
 Johnson Solid: J4
 Vertices: 12
 Faces: 10
 Edges: 20

Also cap of a Rhombicuboctahedron.
Pentagonal Cupola 
 Johnson Solid: J5
 Vertices: 15
 Faces: 12
 Edges: 25
 V: s^{3} / 6 * (5+4*√5)
 A: s^{2} / 4 * (20+√(10*(80+31*√5+√(2175+950*√5))))

Also cap of a Rhombicosidodecahedron.
Pentagonal Rotunda 
 Johnson Solid: J6
 Vertices: 20
 Faces: 17
 Edges: 35
 V: s^{3} / 12 * (45+17*√5)
 A: s^{2} * 5/2 * (√3+√(26+(58/√5)))
 h: s * √(1/5*(5+2*√5))

Also 1/2 of a Icosidodecahedron.
Elongated Triangular Pyramid 
 Johnson Solid: J7
 Vertices: 7
 Faces: 7
 Edges: 12

Elongated Square Pyramid 
 Johnson Solid: J8
 Vertices: 9
 Faces: 9
 Edges: 16

Elongated Pentagonal Pyramid 
 Johnson Solid: J9
 Vertices: 11
 Faces: 11
 Edges: 20

Gyroelongated Square Pyramid 
 Johnson Solid: J10
 Vertices: 9
 Faces: 13
 Edges: 20

Gyroelongated Pentagonal Pyramid 
 Johnson Solid: J11
 Vertices: 11
 Faces: 16
 Edges: 25

Triangular Dipyramid 
 Johnson Solid: J12
 Vertices: 5
 Faces: 6
 Edges: 9

Pentagonal Dipyramid 
 Johnson Solid: J13
 Vertices: 7
 Faces: 10
 Edges: 15
 V: s^{3} / 12 * (5 + √5)
 A: s^{2} * 5/12 * √3
 r_{outer}: s / 10 * √(50+10*√5)
 h: s / 10 * √(5010*√5)

Elongated Triangular Dipyramid 
 Johnson Solid: J14
 Vertices: 8
 Faces: 9
 Edges: 15

Elongated Square Dipyramid 
 Johnson Solid: J15
 Vertices: 10
 Faces: 12
 Edges: 20

Elongated Pentagonal Dipyramid 
 Johnson Solid: J16
 Vertices: 12
 Faces: 15
 Edges: 25

Gyroelongated Square Dipyramid 
 Johnson Solid: J17
 Vertices: 10
 Faces: 16
 Edges: 24
 V: s^{3} * 2^{(1/4)} / 4 * (1 + √2 + 2^{(1/4)} )
 A: s^{2} * 4 * √3

Elongated Triangular Cupola 
 Johnson Solid: J18
 Vertices: 15
 Faces: 14
 Edges: 27

Elongated Square Cupola 
 Johnson Solid: J19
 Vertices: 20
 Faces: 18
 Edges: 36

Elongated Pentagonal Cupola 
 Johnson Solid: J20
 Vertices: 25
 Faces: 22
 Edges: 45

Elongated Pentagonal Rotunda 
 Johnson Solid: J21
 Vertices: 30
 Faces: 27
 Edges: 55

Very suitable for a habitat, the top smaller pentagon as skylight, and eventually the side pentagons further triangulated each.
Gyroelongated Triangular Cupola 
 Johnson Solid: J22
 Vertices: 15
 Faces: 20
 Edges: 33

Gyroelongated Square Cupola 
 Johnson Solid: J23
 Vertices: 20
 Faces: 26
 Edges: 44

Gyroelongated Pentagonal Cupola 
 Johnson Solid: J24
 Vertices: 25
 Faces: 32
 Edges: 55

Next Page >>
Content:  Page 1: Introduction, Platonic Solids, Archimedean Solids, Tetrahedron, Truncated Tetrahedron, Octahedron ...
 Page 2: Johnson Solids
 Page 3: Square Pyramid, Historic Pyramids, Pentagonal Pyramid, Triangular Cupola, Square Cupola, Pentagonal Cupola ...
 Page 4: Gyroelongated Pentagonal Rotunda, Gyrobifastigium, Triangular Orthobicupola, Square Orthobicupola ...
 Page 5: Augmented Triangular Prism, Biaugmented Triangular Prism, Triaugmented Triangular Prism ...
 Page 6: Parabigyrate Rhombicosidodecahedron, Metabigyrate Rhombicosidodecahedron, Trigyrate Rhombicosidodecahedron ...
 Page 7: Uniform Polyhedra, References
 Page 8: Waterman Polyhedra, Some More Examples, Different Origins, Features of Waterman Polyhedra ...
