Ad Quadratum Construction and Study of the Regular Polyhedra
Ad Quadratum Construction and Study of the Regular Polyhedra
Ad Quadratum Construction and Study of the Regular Polyhedra
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Now, as has just been established, <strong>the</strong> edge <strong>of</strong> <strong>the</strong> GI as shown in fig. 45 <strong>and</strong> fig. 58 is:<br />
which can be written:<br />
The scale factor to consider is <strong>the</strong>refore<br />
or, replacing from above:<br />
83<br />
a dod12 a dod 3<br />
S f 8a ic<br />
a dod 3<br />
S f 8<br />
3<br />
with cos I i<br />
2 <br />
3 cos I i<br />
2<br />
<br />
2<br />
it comes<br />
8 3<br />
S f <br />
2 2<br />
After some calculations <strong>and</strong> reduction we have:<br />
8 3<br />
S f 2.7826<br />
11 7<br />
This is <strong>the</strong> number we should multiply measurements on say fig. 45 to find <strong>the</strong> actual<br />
dimension on a model having for kernel <strong>the</strong> icosahedron <strong>of</strong> edge a ic .<br />
The question is what is <strong>the</strong> size <strong>of</strong> <strong>the</strong> original kernel icosahedron that would give rise to<br />
<strong>the</strong> GI built on <strong>the</strong> dodecahedron we started with.<br />
We have designated its edge as <br />
a ic so that we can write:<br />
8a ic<br />
a dod 3<br />
3 <br />
or a ic 8 a dod<br />
<br />
2 1<br />
a dod<br />
8<br />
1<br />
a dod 0.5295a dod<br />
4<br />
8