Truncate a vertex of a Platonic solid a

Truncate a vertex of a Platonic solid and you get a face that fits the Platon...
Tim HuttonTim Hutton - 2014-03-04 16:01:50+0000 - Updated: 2014-03-05 06:53:48+0000
Truncate a vertex of a Platonic solid and you get a face that fits the Platonic solid below it (if there is one). That's a remarkable property. Is there a reason for it, or just coincidence?
Originally shared by Henry SegermanRubenstein's cactus, joint work with +Rick Rubenstein. This is based on a pattern in the truncations of the Platonic solids.

Joint work with Rick Rubenstein. Available from Shapeways at http://shpws.me/r1iO

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Henry Segerman - 2014-03-05 04:45:36+0000
I think it's just a coincidence. It doesn't work for the 4-dimensional regular polytopes. 

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