Posts

Showing posts from September, 2014

Polytope Jewelry

Polytope Jewelry

I just ran across this jewelry collection by Lynne MacLachlan called "Bubble".  She leveraged the software Jenn3D, rapid prototyping, and jewelry techniques to make some beautiful pieces!  

l think the necklace in this image is a dodecahedral prism.  There is also a hypercube based ring and more.  I haven't figured out what the large necklace is yet.  Anyone recognize it?

Jenn3D is free, opensource and available at http://www.math.cmu.edu/~fho/jenn/.
http://lynnemaclachlan.co.uk/blogs/collections/8040689-bubble

A sunflower at infinity

Image
Originally shared by John Baez

A sunflower at infinity

This picture by Roice Nelson shows the 'view at infinity' of a honeycomb in hyperbolic space.

A honeycomb is a way of chopping space into polyhedra.  For example, we can chop ordinary 3d space into cubes.  This is called the {4,3,4} honeycomb.  Why?

• a square has 4 sides so its symbol is {4}

• a cube has 3 squares meeting at each corner so its symbol is {4,3}

• the cubical honeycomb has 4 cubes meeting at each edge so its symbol is {4,3,4}

The picture here is a view of the {3,3,7} honeycomb.  This is defined in the same sort of way, but it doesn't fit into ordinary Euclidean space.  It fits into a curved space called hyperbolic space!   The honeycomb extends forever, and it forms this pattern where it meets the 'plane at infinity' of hyperbolic space.

For links to related pictures, visit my American Mathematical Society blog Visual Insight:

http://blogs.ams.org/visualinsight/2014/09/01/intersection-of-337-honeycomb-and…