The 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

 

Imaging the Tetrahedron:

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

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

ancient celtic model of the tetrahedron, carved in stone

an artist's conceptualization of the tetrahedron

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.

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