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

The Five Platonic Solids; The Cube, or Hexahedron

The Cube at a Glance

Number of faces:
6 squares
Number of edges:
12
Number of vertices:
8
Dihedral angle:
90'
Facial angle:
90'
Central angle:
70'32"
Elemental attribution:
Earth
Geometric dual:
octahedron

Visualizing the Cube

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 cube, carved in stone

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

An artist's conceptualization of the cube

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 cube from cardstock

Proportions within the Cube

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

Insphere
Interspere
Circumsphere
Surface Area
0.5
0.707106781
0.866025404
 
1 divided by 2
1 divided by 
the square root
of 2
the square root
of 3 divided by 2
 
 
Proportions relative to insphere (if insphere radius equals one)
 Edge Length
Intersphere
Circumsphere
Surface Area
2
1.414213562
1.732050808
 
 
square root of 2
 square root of 3
 
 
Proportions relative to intersphere (if intersphere radius equals one)
 Edge Length
Insphere
Circumsphere
Surface Area
1.414213562
0.707106781
1.224744871
 
square root of 2
1 divided by
the square root
of 2
square root of 3
divided by the 
square root 
of 2
 
 
Proportions relative to circumsphere 
(if circumsphere radius equals one)
Edge Length
Insphere
Intersphere
Surface Area
1.154700538
0.577350269
0.816496581
 
four thirds times (the square root
of 3 divided by 2)
1 divided by 
the square root
of 3
the square root
of 2 divided by
the square root
of 3
 

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