Archimedean Solids · 3D

Snub Dodecahedron

3.3.3.3.5 · sr{5,3}

Twelve pentagons, each ringed by triangles and twisted, eighty triangles in all: the most faces of any Archimedean solid, in a left and a right hand.

Turn it in your hands, strike it to hear the chord of its edges, slice it with a plane.

Facts

Four triangles and a pentagon meet at every corner (3.3.3.3.5).
Its 92 faces are the most of any Archimedean solid.
Its corners cannot be written with square roots alone: they hang on the root of a cubic. Here the first corner is solved for, and the icosahedron’s sixty turns place the rest.
It is chiral: toggle the twin to see its mirror image, which no turn can reach.