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Dissect a triangle into smaller triangles, such that all have full edge contact with their neighbors. Label the corners 1, 2, and 3. Label all vertices with 1, 2, or 3, with ...

A torus with a hole that can eat another torus. The transformation is continuous, and so can be achieved by stretching only without tearing or making new holes in the tori.

In this illusion, the vertical lines in the above figure are parallel, but appear to be tilted at an angle. In 1860, F. Zöllner sent his discovery in a letter to physicist ...

The bull graph is a simple graph on 5 nodes and 5 edges whose name derives from its resemblance to a schematic illustration of a bull or ram (whose face is the triangle and ...

The Errera graph is the 17-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof ...

The Gray graph is a cubic semisymmetric graph on 54 vertices. It was discovered by Marion C. Gray in 1932, and was first published by Bouwer (1968). Malnič et al. (2002) ...

The great rhombicuboctahedral graph is the cubic Archimedean graph on 48 nodes and 72 edges that is the skeleton of the great rhombicuboctahedron as well as the great ...

The smallest possible number of vertices a polyhedral nonhamiltonian graph can have is 11, and there exist 74 such graphs, including the Herschel graph and the Goldner-Harary ...

The kite graph is the 5-vertex graph illustrated above (Brandstädt et al. 1987, p. 18). It is implemented in the Wolfram Language as GraphData["KiteGraph"]. Unfortunately, ...

The Paulus graphs are the 15 strongly regular graphs on 25 nodes with parameters (nu,k,lambda,mu)=(25,12,5,6) and the 10 strongly regular graphs on 26 nodes with parameters ...