In geometry, the small stellated dodecahedron is a Kepler–Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol {5⁄2,5}.

It also shares the same edge arrangement with the great icosahedron, with which it forms a degenerate uniform compound figure.

The small stellated dodecahedron can be constructed analogously to the pentagram, its two-dimensional analogue, via the extension of the edges (1-faces) of the core polytope until a point is reached where they intersect.

This observation, made by Louis Poinsot, was initially confusing, but Felix Klein showed in 1877 that the small stellated dodecahedron could be seen as a branched covering of the Riemann sphere by a Riemann surface of genus 4, with branch points at the center of each pentagram.

acts as automorphisms[1] A small stellated dodecahedron can be seen in a floor mosaic in St Mark's Basilica, Venice by Paolo Uccello c. 1430.

The truncated small stellated dodecahedron can be considered a degenerate uniform polyhedron since edges and vertices coincide, but it is included for completeness.