Possible Paper Polyhedra

[MythMath]

The Great Dodecahedron



http://i133.photobucket.com/albums/q48/MythMath/GreatDodecahedronmodelcopy.jpg

[Radiant Star]

The Great Dodecahedron looks like someone I know, Michelin Man even lol

[MythMath]

I was visualizing something decidedly more avian:

http://mpc.byu.edu/data/5/images/8267379632902172497982116.jpg

http://www.nih.gov/news/NIH-Record/12_11_2001/images/native1.jpg

http://www.statemuseum.arizona.edu/images/paint-post/avery/2000-186-228_fr_md.jpg

http://www.autographedtoyou.com/celebpics/famous_chicken2.jpg

lol, I just noticed the star on his jersey...

.

[MythMath]

Okay, I've been building a few cuboctahedra lately:

http://upload.wikimedia.org/wikipedia/en/a/ab/Cuboctahedron.gif

http://i133.photobucket.com/albums/q48/MythMath/Cuboctahedron.jpg
http://en.wikipedia.org/wiki/Cuboctahedron
__________________________________________________ _

The cuboctahedron has 6 square faces and 8 equilateral triangle faces and it makes
a great template for an even more elaborate 3D talisman form based on this idea:

http://i133.photobucket.com/albums/q48/MythMath/SquareTritalisman.jpg

I've been working with this 9-chambered Lo Shu/Tetractys version, but
the 16-unit Jupiter models were described by m1thr0s in the sigil thread:

http://forums.abrahadabra.com/showpost.php?p=13305&postcount=41

[imagenerator]

Yay for polyhedra ! MythMan, have you ever tried to draw/paint/print images for the faces of the polyhedra ? I'm curious to know where other people might take this concept (some context for those unfamiliar: I have designed some images meant for 3D shapes here: http://playful-geometer.deviantart.com). Although I followed that magick square sigil thread, I haven't worked with the pyramid concept yet.

[MythMath]

Here's a scan of one of my little Abrahadabra-inspired cuboctahedra:

http://i133.photobucket.com/albums/q48/MythMath/Cuboctahedronpapercopy.jpg

And here's a refined version of a graph from a few posts ago, that
more clearly reveals the interior geometry of this compelling form:

http://i133.photobucket.com/albums/q48/MythMath/ClearCuboctahedron.jpg

One more bit of related trivia:

http://mathworld.wolfram.com/images/eps-gif/CubicClosePackingCluster_500.gif
http://mathworld.wolfram.com/images/eps-gif/CubicClosePackingCuboct_500.gif


Imagine a sphere surrounded by 12 other spheres.

A collection of 13 such spheres gives the cluster illustrated above.
Connecting the centers of the external 12 spheres gives a cuboctahedron.

Clicking this link: cubic close packing (http://mathworld.wolfram.com/CubicClosePacking.html) , will show how the cuboctahedron
is 3-dimensionally related to our old friend the Merkabah, or stella octangula. (http://mathworld.wolfram.com/StellaOctangula.html)

From: http://mathworld.wolfram.com/Cuboctahedron.html

[MythMath]

http://i133.photobucket.com/albums/q48/MythMath/CuboctahedronAtomicon4colorsfinal.jpg

The framework's structure is essentially hexagons arranged
in a manner that's reminiscent of the Atomicon...

3-D Seed of Life...?

http://www.harmonicwellness.com/seed.jpg

[m1thr0s]

interesting. has a *house-like* feel about it to me...

needs a chimney...lol

m1thr0s