Gerling's 12-Piece Dissection of an Irregular Tetrahedron into Its Mirror Image

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This Demonstration shows Gerling's (1844) dissection of an irregular tetrahedron into 12 symmetrical tetrahedra using a circumscribed sphere. The vertices of a piece are two vertices of the tetrahedron, the center of the circumscribed sphere and the orthogonal projection of the center on a face. The pieces can be reassembled into the tetrahedron's mirror image.

Contributed by: Izidor Hafner (March 2011)
Open content licensed under CC BY-NC-SA



G. N. Frederickson, Dissections: Plane & Fancy, New York: Cambridge University Press, 1997, 2002 p. 231.

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