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the lessor maze

Nov 08, 1993 12:55 PM
by eldon

I have just sent via email to John Mead the file 'big.ig3',
which I would like to make available to the list. I've
asked him to post a notice about its availability after
he has put it into our "theos-l" library. Following is a
description of the file's contents, and a little about
its background.


In his many books on Theosophy, L. Gordon Plummer explores
the platonic solids, and shows how they all interrelate. He
describes them as forming the pattern of the universe, and
creates what he calls the "lessor maze".

It is composed of an icosahedron, enclosing a dodecahedron,
in which are inscribed five cubes. Each cube has a pair
of interlacing tetrahedrons, which each enclose an octahedron.
In all, there are 22 objects:

    1 icosahedron
    1 dodecahedron
    5 cubes
    5 upward tetahedrons
    5 downward tetahedrons
    5 octahedrons

The lessor maze is constructed from 62 points: 20 on the
dodecahedron, 12 on the icosahedron, and 5 x 6 points from the
centers of the faces of the five cubes in the dodecahedorn.

I have created a three-dimensional model using Design Cad,
then converted it to an 3-D IGES file.

Each object is defined in a different drawing plane in the CAD
model.  An objects is formed by a collection of polygons
(triangles, squares, or pentagons), positioned in three
dimensions, specified by the coordinates of its points. For
example, one triangle on the icosahedron is positioned at points

    -2.618, 1.618, 0.000
     1.618, 0.000,-2.618
     2.618,-1.618, 0.000

and 30 triangles are necessary to specify the icosahedron.

In order to make the coordinates as simple as possible, the
whole model is build up around a cube at +-1.000, +-1.000,
+-1.000, around which the dodecahedron is formed.

To prepare various drawings from the lessor maze:

(1) a copy of the whole model can be rotated and scaled

(2) various planes, containing the different objects, can be
    hidden, so that only some of the objects are shown, and

(3) the whole model can be copied and scaled smaller, to show a
    smaller icosahedron and dodecahedron within the bigger ones.

The problem that I am currently working with, is how to
convert, touch up, and make printable the resulting illustrations
from the CAD program. It could be a few months before all the
technical details are worked out, and I am able to include them
in Gordon Plummer's new book, "Three Steps to Infinity."

Anyone interested in experimenting with the model can pick it
up from, according to John Mead's instructions
for getting files from our libraries.

If anyone is able to make some good postscript illustrations
out of the model, please let me know how you did it, and send
me a copy for possible inclusion in Gordon Plummer's book!


                           Eldon Tucker (

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