Pohlke-Schwarz theorem

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Any complete plane quadrilateral can serve as the parallel projection of a tetrahedron similar to a given one.

The theorem was first stated in a different form by K. Pohlke (1853), and was generalized by H.A. Schwarz (1864).


[1] P.S. Alexandroff [P.S. Aleksandrov] (ed.) et al. (ed.) , Enzyklopaedie der Elementarmathematik , 4. Geometrie , Deutsch. Verlag Wissenschaft. (1967) (Translated from Russian)
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Pohlke-Schwarz theorem. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article