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polyhedra

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Project by H_Stevens posted 11-18-2018 07:12 PM 458 views 0 times favorited 3 comments Add to Favorites Watch

Last weekend I was doing a demonstration for some woodworkers on how to build simple polyhedral shapes. Specifically, I showed how to build a Dodecahedron. One of the pictures shows the simple Dodecahedron that I built.

Interestingly in cutting the pentagonal pieces for the Dodecahderon there were 2 pieces on drop. From one of the pieces of drop I was able to construct a Small Stellated Dodecahedron. The second piece of drop formed an object for which I have not be able to find a name.

With respect to Small Stellated Dodecahedron, the base object is a dodecahedron (12 pentagons). Each pod is composed of 5 pieces that have a pentagonal base. There are 12 pods. All miters are at 31.7175 deg.

-- Hamp, St. Simons Island, GA http://hampstevens.com/





3 comments so far

View Phil32's profile

Phil32

266 posts in 104 days


#1 posted 11-18-2018 09:48 PM

Interesting! I have carved some polyhedrons in relief, but not 3-D (yet). Here’s some examples:

-- Phil Allin - Ventura, CA

View Dark_Lightning's profile

Dark_Lightning

3342 posts in 3309 days


#2 posted 11-24-2018 01:46 AM

Interesting! I can’t really tell from the pictures, but does the unidentified one have six-sided facets (when looking at one face) surrounded by five-sided facets, and five-sided facets (when looking at one face) surrounded by six-sided facets, where “facet” means where the glued-on pieces meet, if I’m making sense? If so, it’s a form of stellated Buckyball. There should be a name for it, regardless. Scrounge through here for some examples-

https://en.wikipedia.org/wiki/Polyhedron

-- Random Orbital Nailer

View Phil32's profile

Phil32

266 posts in 104 days


#3 posted 11-24-2018 08:07 PM

Most of these are what you or Wikipedia would define as stellations, but for Escher they were nested polyhedrons. The two chameleons in the first example are caged inside three nested octahedrons. One octohedron is like two 4-sided pyramids arranged base to base. The other two octahedrons are the same size as the first, and are rotated 60 degrees inside the first. The second example (on the tower in “Waterfall”) consists of three nested cubes. The other tower (not shown here) has three nested tetrahedrons. In the third example is a “simple” dodecahedron.

-- Phil Allin - Ventura, CA

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