#snub cube

The faceted snub cube shown above is colored by face type. The one below has faces colored by number of sides, with red triangles and yellow quadrilaterals. Here’s the dual of this particular faceting, shown in “rainbow color mode.” I made these virtual polyhedron models using Stella 4d, which you can try for free right here.

Propaganda

Snub Cube:

Also called the Snub Cuboctahedron

Archimedean Solid

Semiregular

Dual of the Pentagonal Icositetrahedron

It has 6 square faces, 32 regular triangular faces, 60 edges, and 24 vertices.

Chiral so it has two forms that are mirror images of each other.

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.

It has both the tumbling block quilt pattern and a five-pointed star on its surface.

Image Credit: Maxim Razin based on Cyp

Today's shape was the archimedian solid "Snub cube".

The snub cube has 38 faces in total - 6 square faces and 32 triangular faces.

It has 60 edges and 24 vertices.

Each vertex is met by 4 triangle faces and 1 square face.

A snub cube is an alteration of a truncated cuboctahedron.

The drawing:

For the isometric projection drawing I started with a truncated cuboctahedron, and continued to alter the truncated cuboctahedron's octagonal faces into square faces.

Propaganda

Truncated Octahedron:

Archimedean Solid

Semiregular

Dual of the Tetrakis Hexahedron

It has 8 regular hexagonal faces, 6 square faces, 36 edges, and 24 vertices.

A space-filling tessellation/honeycomb of Euclidean three-space.

Image Credit: Cyp

Snub Cube:

Also called the Snub Cuboctahedron

Archimedean Solid

Semiregular

Dual of the Pentagonal Icositetrahedron

It has 6 square faces, 32 regular triangular faces, 60 edges, and 24 vertices.

Chiral so it has two forms that are mirror images of each other.

Propaganda

Sphere:

"Formally, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space." — Wikipedia

Not a convex polyhedron.

Image Credit: Tumblr

Snub Cube:

Also called the Snub Cuboctahedron

Archimedean Solid

Semiregular

Dual of the Pentagonal Icositetrahedron

It has 6 square faces, 32 regular triangular faces, 60 edges, and 24 vertices.

Chiral so it has two forms that are mirror images of each other.

Propaganda

Snub Cube:

Also called the Snub Cuboctahedron

Archimedean Solid

Semiregular

Dual of the Pentagonal Icositetrahedron

It has 6 square faces, 32 regular triangular faces, 60 edges, and 24 vertices.

Chiral so it has two forms that are mirror images of each other.

Image Credit: Cyp

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

Propaganda

Snub Cube:

Also called the Snub Cuboctahedron

Archimedean Solid

Semiregular

Dual of the Pentagonal Icositetrahedron

It has 6 square faces, 32 regular triangular faces, 60 edges, and 24 vertices.

Chiral so it has two forms that are mirror images of each other.

Image Credit: Cyp

Icosidodecahedron:

Archimedean Solid

Quasiregular

Dual of the Rhombic Triacontahedron

It has 12 regular pentagonal faces, 20 regular trianglar faces, 60 edges, and 30 vertices.

Vertex Transitive AND Edge Transitive