In the last post, I showed that five rhombic triacontahedra can be stuck together to form a pentagonal ring. The next logical step is shown here: using such pentagonal rings to construct an entire dodecahedron made of rhombic triacontahedra.

Software credit: see http://www.software3d.com/stella.php.

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Hi Robert

This One Is SPECIAL.

Is that 5 pentagonal rings for a total of 25?

300 surfaces – 18 = 292 surfaces ??

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Thanks again! There are 20 rhombic triacontahedra in this figure. Each normally has 30 faces each, but only 27 are uncovered here, so there are (20)(27) = 540 faces exposed in the whole thing.

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