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Engel Polyhedra

EngelPolyhedron

The Engel polyhedra are two 38-faced plesiohedra (and hence space-filling) discovered by Engel (Engel 1981; Engel 1986, p. 220; Grünbaum and Shephard 1980; Senechal 1990, Fig. 1.14, p. 14; Pegg 2022). Engel's polyhedra are known to have the largest possible number of faces for a plesiohedron (Schmitt 2016). One of the two is shown above in a particular embedding as constructed by Pegg (2022).

See also

Plesiohedron, Space-Filling Polyhedron

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References

Engel, P. "Über Wirkungsbereichsteilungen von kubischer Symmetrie." Zeit. für Kristallographie, Kristallgeometrie, Kristallphysik, Kristallchemie 154, 199-215, 1981.Engel, P. Geometric Crystallography: An Axiomatic Introduction to Crystallography. Dordrecht, Netherlands: Reidel, 1986.Grünbaum, B. and Shephard, G. C. "Tilings With Congruent Tiles." Bull. Amer. Math. Soc. 3, 951-973, 1980.Pegg, E. "Engel 38-Sided Space-Filling Polyhedron." 2022. https://community.wolfram.com/groups/-/m/t/2617634.Schmitt, M. W. "On Space Groups and Dirichlet-Voronoi Stereohedra." Doktors der Naturwissenschaften Dissertation. Berlin: Freien Universität Berlin, 2016. https://refubium.fu-berlin.de/handle/fub188/10176.Senechal, M. Crystalline Symmetries: An Informal Mathematical Introduction. Boca Raton, FL: CRC Press, 1990.

Cite this as:

Weisstein, Eric W. "Engel Polyhedra." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EngelPolyhedra.html

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