nature's word : musings on sacred geometry

The Icosahedron

 The Icosahedron at a Glance

Number of faces:

20 triangles

Number of edges:

30

Number of vertices:

12

Dihedral angle:

138’11”

Facial angle:

60′

Central angle:

63’26”

Elemental attribution:

Water

Geometric dual:

dodecahedron

 

 

 Imaging the Icosahedron:

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

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


ancient celtic model of the icosahedron, carved in stone


an artist’s conceptualization of the icosahedron


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

 

 

Proportions within the Icosahedron

 

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

Insphere

Intersphere

Circumsphere

Surface Area

0.755761314

0.809016994

0.951056516

 

 

phi divided by 2

 

 

 

Proportions relative to insphere (if insphere radius equals one)

 Edge Length

Intersphere

Circumsphere

Surface Area

1.323169076

1.070466269

1.258408572

 

 

1 divided by

(phi divided by the square root

of 3)

 

 

 

Proportions relative to intersphere (if intersphere radius equals one)

 Edge Length

Insphere

Circumsphere

Surface Area

1.236067978

0.934172359

1.175570505

 

1 divided by 

(phi divided by 2)

phi divided by the

square root of 3

 

 

 

Proportions relative to circumsphere 

(if circumsphere radius equals one)

Edge Length

Insphere

Intersphere

Surface Area

1.051462224

0.7946654472

0.850650808

 

 

 

 

 

 

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


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