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.

back to top