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Plesiohedron


Plesiohedra

A plesiohedron is the Voronoi cell of a so-called symmetric Delone set. Plesiohedra are space-filling polyhedra which have special symmetries that take any copy of the plesiohedron in the space-filling honeycomb to any other.

The five parallelohedra are plesiohedra, as are the triangular prism, plesiohedral gyrobifastigium, triakis truncated tetrahedron, and trapezo-rhombic dodecahedron.

EngelPolyhedron

Other plesiohedra include the 17-sided Voronoi cells of the Laves graph and two 38-faced polyhedra Engel polyhedra, one of which is illustrated above (Pegg 2022). The latter are known to have the largest possible number of faces for a plesiohedron (Schmitt 2016).


See also

Engel Polyhedra, Space-Filling Polyhedron

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References

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.

Cite this as:

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

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