The hemi-dodecahedron is the regular map on the real projective plane obtained by identifying
opposite vertices, edges,
and faces of a regular
dodecahedron (Leemans and Schulte 2007). The resulting map has 10 vertices,
15 edges, and six pentagonal faces. Its type is denoted 
, with the subscript giving the length of a Petrie polygon (Leemans and Schulte 2007). Its skeleton is the Petersen
graph (Séquin and Lanier 2007).
The dual map is obtained by the same identification in the regular icosahedron. The hemi-dodecahedron
is the vertex figure of the 11-cell
and each facet of the 57-cell
(Coxeter 1982, Leemans and Schulte 2007).
See also
11-Cell,
57-Cell,
Petersen Graph,
Real
Projective Plane,
Regular Dodecahedron,
Regular Map
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References
Coxeter, H. S. M. "Ten Toroids and Fifty-Seven Hemi-Dodecahedra." Geom. Dedicata 13, 87-99, 1982. https://doi.org/10.1007/BF00149428.Leemans,
D. and Schulte, E. "Groups of Type 
Acting on Polytopes." Adv. Geom. 7,
529-539, 2007. https://doi.org/10.1515/ADVGEOM.2007.031.Séquin,
C. H. and Lanier, J. "Hyperseeing the Regular Hendecachoron." In Proc.
6th Interdisciplinary Conf. of the International Society of the Arts, Mathematics,
and Architecture. pp. 161-168, 2007. https://graphics.berkeley.edu/papers/Sequin-HRH-2007-05/Sequin-HRH-2007-05.pdf.
Cite this as:
Weisstein, Eric W. "Hemi-Dodecahedron."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Hemi-Dodecahedron.html
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