Shop Forum More Submit  Join Login
Twistohedra by Hop41 Twistohedra by Hop41
5 solids from a continuum of solids having the rotational symmetry of the icosohedron and dodecahedron Platonic solids.

The "integers" of this continuum will also have the mirror plane symmetries of these solids. But the non-integers will be chiral.

For more on these solids see: [link]
Add a Comment:
 
:iconorientalarc:
OrientalArc Featured By Owner May 20, 2013  Hobbyist Interface Designer
looks very intriguing..
Reply
:iconidoux:
iDoux Featured By Owner Feb 7, 2013  Hobbyist Artisan Crafter
Really dont understand much of the math science behind this, but it looks awesome, are you math teacher or something?
Reply
:iconhop41:
Hop41 Featured By Owner Feb 7, 2013
Thanks! No, I'm not a math teacher, just someone who loves math. Hopefully my art will teach folks some math and geometry, though.
Reply
:iconidoux:
iDoux Featured By Owner Feb 7, 2013  Hobbyist Artisan Crafter
No problem, and having fun while learning!
Reply
:iconsofirr:
sofirr Featured By Owner Sep 18, 2012  Hobbyist Traditional Artist
Oh ...great!
Reply
:iconhop41:
Hop41 Featured By Owner Sep 18, 2012
Thanks!
Reply
:iconikarusmedia:
ikarusmedia Featured By Owner Feb 24, 2012
marvelous, how did you figure out how to make them fit?
Reply
:iconhop41:
Hop41 Featured By Owner Feb 25, 2012
While all the top solids have the same center to vertice radius, I had to shrink the nested solids to get them to fit inside each other. Not much, just subtracting multiples of cardboard thickness.

I forget the detailed math, but I usually consult Coxeter's "Regular Polytopes" [link] when doing this sort of thing. Coxeter sets edge length = 2s and from there uses the Pythagorean Theorem and trigonometry to work out other lengths within the polygons and polyhedra in terms of s. It's a Dover book so it's pretty inexpensive.
Reply
:iconikarusmedia:
ikarusmedia Featured By Owner Feb 26, 2012
wow!, thanks for the explanation. while checking some of the pages of the book in amazon it seems advanced for me because i do not know anything about trigonometry but looks interesting nonetheless.
Reply
:iconink-dreamsmmix:
Ink-DreamsMMIX Featured By Owner Jan 25, 2011  Hobbyist General Artist
Woosssh, your description went right over my head:), very impressive paper cutting though.
Reply
:iconbear48:
bear48 Featured By Owner Jul 19, 2010  Professional
sweet
Reply
:iconrndmodels:
RNDmodels Featured By Owner May 11, 2010  Professional Artisan Crafter
great job twistohedra, your lines and edges came out great! This is the same geometry as my dodecahedron / icosahedron 'dual' model except that you added the links that also show the rhombic triacontahedron. My next go around will have all three yet made from wood stained 3 colors to show them apart.
-Ron
Reply
:iconhappymouse666:
happymouse666 Featured By Owner Mar 29, 2009  Professional General Artist
I love making stuff out of paper. These crazy math models are wild. I have been playing with this free 3d program for making things like this for the last week or so. You would probably enjoy it. It is really easy to figure out. Check it out.


[link]
Reply
:iconoixstudios:
OIXstudios Featured By Owner Mar 22, 2009
Wow this is Paper ingenairy? awesome and complex stand allone he he he he
Reply
:iconvidthekid:
vidthekid Featured By Owner Mar 22, 2009  Hobbyist Digital Artist
I like -1 the best.
Reply
Add a Comment:
 
×




Details

Submitted on
March 20, 2009
Image Size
68.6 KB
Resolution
576×860
Link
Thumb

Stats

Views
1,970 (1 today)
Favourites
45 (who?)
Comments
15
Downloads
41