The second coffee table is to have an Icosahedron outer shape and a regular Dodecahedron within. Here are some illustrations. The Icosahedron is shown with blue struts and golden/orange spherical vertices/hubs. The regular Dodecahedron is shown with red struts and small golden/orange spherical vertices/hubs. Very thin green struts join the outer Icosahedron to the inner Dodecahedron.
An Icosahedron has 12 vertices, 20 triangular faces and 30 edges/struts. There are 5 struts converging at each hub.
A regular Dodecahedron has 20 vertices, 12 pentagon faces and 30 edges/struts. There are 3 struts converging at each hub.
If you extend the edges/struts of the Dodecahedron beyond the Dodecahedron's vertices, you find that they merge in 20 groups of 3. These in new merged/intersection points define the vertices of an Icosahedron.
Height (without glass): 16.0 inches = 15 inches Icosahedron + 2x0.5 inches radius of hubs.
Glass thickness: 0.25 inches.
Total Height (including glass top): 16.25 inches.
The Icosahedrons hubs are to be made out of 1 inch diameter spherical wooden spheres.
The Dodecahedron's hubs are to be made out of 0.5 inch diameter spherical wooden spheres.
Icosahedron Struts (need 30): 0.5 inches diameter.
Vertex to Vertex length (i.e., center of hub to center of hub): 9.924 inches.
InterPolyhedron Struts (need 60): 0.125 inches diameter.
Vertex to Vertex length: 6.133 inches.
(NOTE: These struts are to be cut “in place” and not pre-cut. This is because
accumulation of error and other factors introduce unpredictable
inaccuracies. These struts are surface glued to the polyhedra hubs, i.e. not
recessed into the hubs.)
The Dodecahedron's hubs are designed as follows.
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| Dodecahedron hub angles. |
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