Penrose tiling on sphere

Radu Sora

unread,

Feb 9, 2016, 9:17:55 AM2/9/16

to Geodesic Help Group

Is there any known solution for that. What about this picture? Seems to have 2 kind of tiles. Is it correct? Parametric function anyone?

Screen Shot 2014-07-26 at 17.12.41.png

TaffGoch

unread,

Feb 9, 2016, 4:42:53 PM2/9/16

to Geodesic Help Group

There is only one "tile" definition. The geometry is the pentagonal hexecontahedron.

http://www.maa.org/community/columns/maa-found-math/week-17

Radu Sora

unread,

Feb 9, 2016, 5:09:36 PM2/9/16

to Geodesic Help Group

Hmm... The good thing is that it looks like an egg tessellation of sphere. The bad thing is that it is limited to 60 faces. Are you sure it cannot be "broken" further?

TaffGoch

unread,

Feb 9, 2016, 5:39:35 PM2/9/16

to Geodesic Help Group

Further, yes, but not with identical tiles. With "similar" tiles, you can tessellate to higher frequencies (just as you can with "apparently equivalent" triangles on a geodesic sphere.)

I've posted 11 different examples, here: Geodesic Floret Tessellations

It has been a topic of discussion, before. Search within the group for "floret"

-Taff

Reply all

Reply to author

Forward