Site Search

If you found the information useful, consider to make a donation:

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 * √(50-10*√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 ...

Creative Commons (CC) BY, SA, NC 2005-2017,
developed, designed and written by
René K. Müller ,
Graphics & illustrations made with
Inkscape ,
Tgif ,
Gimp ,
PovRay ,
GD.pm
Web-Site powered by FreeBSD & Debian/Linux - 100% Open Source