Contact the author:
aoconnor|at|unitone|dot|org

The Platonic Solids
...the Icosahedron

 The Icosahedron at a Glance

Number of faces:
20 triangles
Number of edges:
30
Number of vertices:
12
Dihedral angle:
138'11"
Facial angle:
60'
Central angle:
63'26"
Elemental attribution:
Water
Geometric dual:
dodecahedron
 
 
 Imaging the Icosahedron:

(IMAGE REMOVED) small, basic animation (poorer quality, shorter download)

(IMAGE REMOVED) larger, more complex animation (higher quality, longer download)


ancient celtic model of the icosahedron, carved in stone


an artist's conceptualization of the icosahedron


net, or pattern, that can be used to create a icosahedron from cardstock

 
 
Proportions within the Icosahedron
 
Proportions relative to edge length (if edge length equals one)
Insphere
Intersphere
Circumsphere
Surface Area
0.755761314
0.809016994
0.951056516
 
 
phi divided by 2
 
 
 
Proportions relative to insphere (if insphere radius equals one)
 Edge Length
Intersphere
Circumsphere
Surface Area
1.323169076
1.070466269
1.258408572
 
 
1 divided by
(phi divided by the square root
of 3)
 
 
 
Proportions relative to intersphere (if intersphere radius equals one)
 Edge Length
Insphere
Circumsphere
Surface Area
1.236067978
0.934172359
1.175570505
 
1 divided by 
(phi divided by 2)
phi divided by the
square root of 3
 
 
 
Proportions relative to circumsphere 
(if circumsphere radius equals one)
Edge Length
Insphere
Intersphere
Surface Area
1.051462224
0.7946654472
0.850650808
 
 
 
 
 
 
 Special thanks to Bruce Rawles for supplying the above listed proportional figures.

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