nature's word : musings on sacred geometry

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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all materials copyright 2010, Aidrian O'Connor