#platonic solids

[todays-xkcd]

Plato made the solids, and five were gifted to the mathematicians. But in secret Plato forged a sixth solid to rule over all the others.

The Six Platonic Solids [Explained]

[aromanticduck]

New nerd/geek diagnostic check. Ask them to identify this shape:

If they say 'icosahedron', they're a nerd.

If they say 'd20', they're a geek.

[best-shapes]

Regular-ish Convex Polyhedra Bracket — Round 5 (Finals)

Propaganda

Truncated Icosidodecahedron:

Also called the Rhombitruncated Icosidodecahedron, Great Rhombicosidodecahedron, Omnitruncated Dodecahedron, Omnituncated Icosahedron

Archimedean Solid

Semiregular

Dual of the Disdyakis Triacontahedron

It has 12 regular decagonal faces, 20 regular hexagonal faces, 30 square faces, 180 edges, and 120 vertices.

It has the most edges and vertices of all platonic and archimedean solids.

Of the vertex-transitive polyhedra, it fills up the most of the volume of the sphere it fits in (89.80%).

It is not actually the shape you get when you truncate an icosidodecahedron, although it is topologically equivalent.

It is the mod's favorite three-dimensional shape.

They made a void truncated icosidodecahedron and it's glorious. I had one for a while, it's hard to turn because of alignment issues, especially the decagonal sides. Fun puzzle tho, never did figure out how to permute the last layer...

Image Credit: @anonymous-leemur

Regular Icosahedron:

Platonic Solid

Regular

Dual of the Regular Dodecahedron

It has 20 regular triangular faces, 30 edges, and 12 vertices.

Image Credit: @etirabys

[knotty-et-al]

Polyhedra on dotted isometric paper

Drawing polyhedra on dotted isometric paper is so calming. One does not need to use a ruler or a compass. Instead one can just count dots to determine the length, and play around with the angles.

[earolinc]

once on this app i saw someone call kepler-poinsot polyhedra queerplatonic solids and that post occupies a significant amount of space in my brain. i think about it daily.

[art-of-mathematics]

Today's Tiny Tetrahedron

(artist of the colorful artwork in the background of the first photo is unknown)

[mycrystalearth]

🌞 abundance & prosperity 🌞

[m---a---x]

your pfp looks cool! is it some sort of 4d polytope?

Oh, cool, my first question!

My pfp is a projection of the 120 cell (4d equivalent of the dodecahedron) with 4 fibres of a hopf fibration highlighted, which is adjacency-equivalent to the (faces of the) dodecahedron

[wormintrouble]

desert wizard and platonic solids

[freyaholmer]

youll get there buddy

[best-shapes]

Regular-ish Convex Polyhedra Bracket — Round 3

Propaganda

Regular Tetrahedron:

Also called the Triangular Pyramid

Platonic Solid

Regular

Dual of the Regular Tetrahedron

It has 4 regular triangular faces, 6 edges, and 4 vertices.

Self-Dual

Image Credit: Cyp

Rhombic Triacontahedron:

Also called the Triacontahedron

Catalan Solid

Dual of a quasiregular polyhedron

Dual of the Icosidodecahedron

It has 30 rhombic faces, 62 edges, and 32 vertices of two types.

One of the 9 edge-transitive convex polyhedra along with the 5 Platonic Solids, the 2 Quasiregular Convex Polyhedra, and the Rhombic Dodecahedron.

Image Credit: Maxim Razin based on Cyp

[knotty-et-al]

A visual study of the Icosahedron inside an Octahedron - and the remaining tetrahedral modules

The tetrahedral modules:

Buckminster Fuller came up with these modules and called them "S modules" or "S quanta modules".

Here is a helpful summary:

[Source (PDF) | A Fuller Explanation: The Synergetic Geometry of R. Buckminster Fuller, 1987]

[earolinc]

"i really love your shirt! the shape on it is an icosahedron, which is a platonic solid"

"you don't get invited to parties, do you?"

[quasi-normalcy]

Plato made the solids, and five were gifted to mathematicians. But in secret, Plato forged a sixth solid to rule over all the others.