The Five Platonic Solids; The Tetrahedron

The Tetrahedron at a Glance

Number of faces:	4 triangles
Number of edges:	6
Number of vertices:	4
Dihedral angle:	70'32"
Facial angle:	60'
Central angle:	109'28"
Elemental attribution:	Fire
Geometric dual:	tetrahedron

Visualizing the Tetrahedron

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 tetrahedron, carved in stone

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

An artist's conceptualization of the tetrahedron

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 tetrahedron from cardstock

Proportions within the Tetrahedron

Proportions relative to edge length (if edge length equals one)

Insphere	Interspere	Circumsphere	Surface Area
0.204124145	0.353553391	0.612372436
	square root of 2 divided by 4

Proportions relative to insphere (if insphere radius equals one)

Edge Length	Intersphere	Circumsphere	Surface Area
4.898979486	1.732050808	3
	square root of 3

Proportions relative to intersphere (if intersphere radius equals one)

Edge Length	Insphere	Circumsphere	Surface Area
2.828427125	0.577350269	1.732050808
8 times (the square root of 2 divided by 4)	1 divided by the square root of 3	square root of 3

Proportions relative to circumsphere (if circumsphere radius equals one)

Edge Length	Insphere	Intersphere	Surface Area
1.632993162	0.33333333	0.577350269
	1 divided by 3	1 divided by the square root of 3

Special thanks to Bruce Rawles for supplying the above listed proportional figures.