THE MAGNETIC DOT ENCYCLOPEDIA

Lattice in hyperbolic space, puffed triangles Like

by: EdoTimmermans Follow


It looks like it might be possible to continue this build forever using the same logic. When you tessellate the dodecahedron it doesn't fit in regular space it doesn't work, as dodecahedra will overlap. However, in hyperbolic space it works. (see the related links in my comment) With dodecahedra you get a finite shape, as the connected dodecahedra quickly get smaller. However, with these triangles, they quickly get larger. And as they are connected with narrow tunnels, you get an infinite structure where you can walk in or outside the tunnel system, as in a lattice. Only here, distances and puffy triangles will get huge quickly as you get further away from the center where the build started.
For some reason my comment with links doesn't come through, so I'll put it here:
Links related to tesselating in hyperbolic space:
http://en.wikipedia.org/wiki/Order-4_dodecahedral_honeycomb
very scientific, no drawings: http://en.wikipedia.org/wiki/Seifertâ??Weber_space
hyperbolic and other math art: http://www.bugman123.com/Hyperbolic/index.html









Comments

  • Gustoph - 2 years ago
    That's what I call thinking outside the box! You truly are gifted Mr. Timmermans! Please keep these wonderful shapes coming! They are in an inspiration, as are you, to myself and magnetic geometrists everywhere! That's my fancy way of saying people who play with their magnets...
    Seriously, you have talent, and it looks like you might know it! You should be incredibly proud of the designs that you've shared with our little community here. Thank you from all of us!