Hessel also found Euler's formula disobeyed with interconnected polyhedra, for example, where an edge or vertex is shared by more than two faces (e.g. as in edge-sharing and vertex-sharing tetrahedra).
Stanley Kubrick originally intended the monolith in 2001: A Space Odyssey to be a tetrahedron, according to Marvin Minsky, a cognitive scientist and expert on artificial intelligence who advised Kubrick on the Hal 9000 computer and other aspects of the movie.
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It is used as album artwork, surrounded by black flames on The End of All Things to Come by Mudvayne.
In addition to toys such as the Hoberman sphere, the largest of which resides at Liberty Science Center in Jersey City, New Jersey, Hoberman created the BrainTwist, a hard plastic tetrahedron that folds, stellates, and becomes self-dual while having a component that rotates similarly to a Rubik's Cube.
Reuleaux tetrahedron, the intersection of four spheres of equal radius centered at the vertices of a regular tetrahedron
The design is reminiscent of the Sierpinski tetrix: placing four half-size tetrahedra corner to corner and adding an octahedron in the middle, a full-size tetrahedron is formed; this process can be repeated recursively to form larger and larger tetrahedra.