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Oscar Cunningham
@OscarCunningham@mathstodon.xyz  ·  activity timestamp 4 days ago

#Mathober #Mathober2025

The prompt for day 3 was 'Polyhedron'. In mathematics a 'convex polyhedron' is any subset of ℝ³ which can be obtained as the convex hull of finitely many noncoplanar points. However, when convexity is not required the definition of 'polyhedron' is in some dispute.

Certainly every convex polyhedron is a polyhedron, however there are multip-

On second thoughts, this post would be better expressed as an alignment chart meme.

#Math #Maths #Mathematics #Geometry #Polyhedra

A three by three grid defining various candidate polyhedra as 'Purist', 'Neutral' or 'Radical' depending on whether the correspond to subsets of ℝ³, and how nice their combinatorial properties are.

The polyhedra are:
Purist/Purist: Cube
Purist/Neutral: Two cubes
Purist/Radical: An octant
Neutral/Purist: An icosahedron deformed so that two of its vertices coincide
Neutral/Neutral: A star dodecahedron
Neutral/Radical: A cube with an additional face on its interior
Radical/Purist: A dihedron (two identical faces glued to each other along all their edges)
Radical/Neutral: Penrose triangle
Radical/Radical: A hemicube (obtained from a cube by quotienting antipodal points)
A three by three grid defining various candidate polyhedra as 'Purist', 'Neutral' or 'Radical' depending on whether the correspond to subsets of ℝ³, and how nice their combinatorial properties are. The polyhedra are: Purist/Purist: Cube Purist/Neutral: Two cubes Purist/Radical: An octant Neutral/Purist: An icosahedron deformed so that two of its vertices coincide Neutral/Neutral: A star dodecahedron Neutral/Radical: A cube with an additional face on its interior Radical/Purist: A dihedron (two identical faces glued to each other along all their edges) Radical/Neutral: Penrose triangle Radical/Radical: A hemicube (obtained from a cube by quotienting antipodal points)
A three by three grid defining various candidate polyhedra as 'Purist', 'Neutral' or 'Radical' depending on whether the correspond to subsets of ℝ³, and how nice their combinatorial properties are. The polyhedra are: Purist/Purist: Cube Purist/Neutral: Two cubes Purist/Radical: An octant Neutral/Purist: An icosahedron deformed so that two of its vertices coincide Neutral/Neutral: A star dodecahedron Neutral/Radical: A cube with an additional face on its interior Radical/Purist: A dihedron (two identical faces glued to each other along all their edges) Radical/Neutral: Penrose triangle Radical/Radical: A hemicube (obtained from a cube by quotienting antipodal points)
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