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> These are solids where all the sides are equal and all the faces are the same regular polygon. There is, for instance, rhombic triacontahedron[1] which fulfi
by a_c 9y ago
> These are solids where all the sides are equal and all the faces are the same regular polygon.
There is, for instance, rhombic triacontahedron[1] which fulfil the above definition while not being a platonic solid.
By wiki[2] ,
> It is constructed by congruent (identical in shape and size) regular (all angles equal and all sides equal) polygonal faces with the same number of faces meeting at each vertex.
[1] https://en.wikipedia.org/wiki/Rhombic_triacontahedron https://en.wikipedia.org/wiki/Rhombic_triacontahedron
[2] https://en.wikipedia.org/wiki/Platonic_solid https://en.wikipedia.org/wiki/Platonic_solid
- bzbarsky 9y agoThe faces there are rhombuses, which are not regular polygons, right? The definition of a regular polygon includes equality of angles, not just of sides.
- a_c 9y agoThanks for pointing out. You are right! It looks silly to have mistaken such a simple concept but let's leave it here in case someone has same thought as me
- Someone 9y ago”platonic solids are solids where all the sides are equal and all the faces are the same regular polygon” is true, but the reverse isn’t. I think you also want all vertices to lie on a single sphere. Without that, you can have various stellated polyhedra, constructions of 6 or 10 equilateral triangles, an infinite number of constructs that only contain squares, and probably others. I also think “all the faces are the same regular polygon” implies “all the sides are equal” for the ‘normal’ definitions of “polyhedron”, but that definition is surprisingly hard. One typically wants to exclude faces crossing each other and constricts that aren’t connected, such as “two cubes”, so who knows?