The Platonic Solids
...the Octahedron

The Octahedron at a Glance

Number of faces:	8 triangles
Number of edges:	12
Number of vertices:	6
Dihedral angle:	109'28"
Facial angle:	60'
Central angle:	90'
Elemental attribution:	Air
Geometric dual:	cube

     Imaging the Octahedron:

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

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

ancient celtic model of the octahedron, carved in stone

an artist's conceptualization of the octahedron

net, or pattern, that can be used to create a octahedron from cardstock

    Proportions within the Octahedron   Proportions relative to edge length (if edge length equals one)

Insphere	Intersphere	Circumsphere	Surface Area
0.40824829	0.5	0.707106781
(the square root of 3 times the square root of 2) divided by 6	1 divided by 2	1 divided by the square root of 2

  Proportions relative to insphere (if insphere radius equals one)

Edge Length	Intersphere	Circumsphere	Surface Area
2.449489743	1.224744871	1.732050808
the square root of 3 times  the square root of 2	the square root of 3 divided by  the square root of 2	square root of 3

  Proportions relative to intersphere (if intersphere radius equals one)

Edge Length	Insphere	Circumsphere	Surface Area
2	0.816496581	1.414213562
	the square root of 2 divided by the square root of 3	square root of 2

  Proportions relative to circumsphere  (if circumsphere radius equals one)

Edge Length	Insphere	Intersphere	Surface Area
1.414213562	0.577350269	0.707106781
square root of 2	1 divided by  the square root of 3	1 divided by the square root of 2

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

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