The Five 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

Visualizing the Icosahedron

click for image creditsOriginal animation created by A. O'Connor for Nature's Word using POV-Ray, WWW Gif Animator, and Adobe Photoshop 5.0.

Basic animation

click for image creditsPhoto of ancient celtic platonic model, carved from stone, taken by Rod Bull. Taken From: Keith Critchlow's book Time Stands Still, St. Matin's Press, 1982

Ancient celtic model of the icosahedron, carved in stone

click for image creditsOriginal artwork by Bob Smith. Used with the artist's permission.

An artist's conceptualization of the icosahedron

click for image creditsscanned image reworked by A. O'Connor in Photoship 5.0, Taken from: Anthony Pugh's book Polyhedra; A Visual Approach

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	Interspere	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.