Day 202 – Triakis Octahedron

Day 202 – Triakis Octahedron

Day 202 – Triakis Octahedron 640 480 mathgrrl

New fact of the day: If you add a pyramid to each face of an octahedron, then you are taking its “Kleetope.” A cool new word for me, leading to the next Catalan solid in our list: the Triakis Octahedron.

Thingiverse link:

Settings: MakerWare custom profile described in Day 194, on a Replicator 2. Sizing was determined using the method from Day 195; at the end of the Catalan series we’ll do a recap, including the sizing parameters for each polyhedron and how they were obtained.

Technical notes, design flavor: The Catalan wireframes I’ve been printing are a bit stylized, with vertices that become larger according to their degree. This is because of the remeshing that I am choosing in TopMod, specifically the “Doo Sabin” remeshing. I went with this because I like that I can easily differentiate between different types of vertices; for example, in today’s model the vertices that belong to the underlying octahedron (before the “kleetoping”) are larger and stand out, while the vertices that form the topes of the added pyramids are smaller. In addition the extra bit around each corner helps make a very stable model that can be dropped on the floor, thrown, and otherwise abused without breaking.

Technical notes, Kleetope flavor: We printed a Kleetope earlier, on Day 199; the Triakis Icosahedron was the Kleetope of the icosahedron. In fact, each of the Platonic solids gives rise to a Kleetope that is a Catlan solid with isosceles-triangular faces:

  • the Triakis Tetrahedron is the Kleetope of the tetrahedron;
  • the Triakis Octahedron is the Kleetope of the octahedron;
  • the Tetrakis Hexahedron is the Kleetope of the cube (a.k.a. the hexahedron);
  • the Pentakis Dodecahedron is the Kleetope of the dodecahedron; and
  • the Triakis Icosahedron is the Kleetope of the icosahedron.
Technical notes, capitalization flavor: I have decided that Catalan solids are cool and deserve to be capitalized, but I can’t bring myself to capitalize my old friends the Platonic solids. Somehow they look silly all dressed up like that. Sorry, capitalization police.

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