Natures Word: Musings on Sacred Geometry
NAURE'S WORD: Title Page FURTHER WORK: COMPARATIVE RELIGION:

The Five 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

Visualizing the Octahedron

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 octahedron, carved in stone

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

An artist's conceptualization of the octahedron

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 octahedron from cardstock

Proportions within the Octahedron

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

Insphere
Interspere
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.