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.
all materials copyright 2010, Aidrian O'Connor
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