"Three objects are spinning so quickly that you only see a blur. The three objects are: a line that rotates to make a hyperboloid, a cube that rotates to make a combination of cones and hyperboloid, and three ellipses that rotate to make a cylinder. Pushing a button stops the spinning to reveal the object."

Geometric patterns on the ceilings of European cathedrals. Photos by David Stephenson.

“Prismatica consists of an arrangement of pyramid-shaped crystals affixed to an LCD screen and illuminated with programmed geometric animation. The animated patterns are precisely mapped to the vertices of the crystals, illuminating them individually and in formation. The animations are further refracted through the geometry of the crystals in accordance with the shifting perspective of the observer, which in turn alters the way the illuminations appear and interact with reflections of surrounding lights within the space.”

An Escher-inspired painting on a sphere. By Dick Termes.

A polyhedron made of a 7/4-Cuploid, 7 triangles, 7 squares, 1 7/3-heptagram

"Girih tiles have interior angles that are multiples of π/5. In the examples shown here I’ve applied the girih concept to polygons with angles that are multiples of π/7."

By Joe Bartholomew

This sculpture is 8 feet in diameter and, from what I can tell, is a compound of five octahedra (a stellation of the icosahedron). The designs are projected onto its surface.

“Parmenides I” by artist Dev Harlan

Discs in geometric proportions cover the unit disc.
From The Geometry Junkyard.

"Equal Areas" by Susan McBurney.
This image, inspired by Leonardo DaVinci, builds upon a concept of equal areas. The sum of the areas of the red shapes in the bordering semicircles is equal to the sum of the areas of the red shapes inside the center circle; and the same goes for the green, yellow, pink, and peach shapes.

Icosahedron by Richard Sweeney

The fourth stellation of an icosahedron

A polyhedron constructed by folding along the edges of a Spidron - a figure in the plane made up of two alternating sequences of isosceles triangles.

Penrose tiling

A rhombic triacontahedron and its net

Impossible Geometry by Jos Leys

"The Easy Way Up" from Impossible Geometry by Jos Leys

A cube 6-compound shows 6 overlapping cubes.

Geometry of Circles by Phillip Glass

Hyperbolic geometry differs greatly from what we are used to in that the longest path between two points is a straight line. You can think of hyperbolic space like Euclidean space, but with a different way of defining the distance between two points (we call this a metric). Above is the hyperbolic equivalent of an icosidodecahedron. Check out more hyperbolic tilings here.

Decagonal trapezohedron