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In 2006, Inchbald described the basic theory of faceting diagrams for polyhedra. For a given vertex, the diagram shows all the possible edges and facets (new faces) which may be used to form facetings of the original hull. It is
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by Frank J. Swetz (2013): "In this study of the five
Platonic solids, Jamnitzer truncated, stellated, and faceted the regular solids "
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685:'s stellation diagram, which shows all the possible edges and vertices for some face plane of the original core.
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290:: small stellated dodecahedron, great dodecahedron, and great icosahedron. They all have 30 edges.
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has two symmetric facetings, one as a polygon, and one as a compound of two triangles.
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will have two faces on each edge and creates new polyhedra or compounds of polyhedra.
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In 1974, Bridge enumerated the more straightforward facetings of the
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Removing parts of a polytope without creating new vertices
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Mathematical
Treasure: Wenzel Jamnitzer's Platonic Solids
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New edges of a faceted polyhedron may be created along
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Comptes rendus des séances de l'Académie des
Sciences
627:which fits inside a cube, and which he called the
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594:Faceting has not been studied as extensively as
726:Note sur la théorie des polyèdres réguliers,
33:Stella octangula as a faceting of the cube
737:Bridge, N.J. Facetting the dodecahedron,
385:is a facetting with star hexagon faces.
49:) is the process of removing parts of a
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97:, there exists a dual faceting of the
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428:Great ditrigonal icosi-dodecahedron
418:Small ditrigonal icosi-dodecahedron
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669:polyhedra, including those of the
286:can be faceted into three regular
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747:Inchbald, G. Facetting diagrams,
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609:Perspectiva Corporum Regularium
113:has one symmetry faceting, the
93:. For every stellation of some
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423:Ditrigonal dodeca-dodecahedron
83:Faceting is the reciprocal or
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765:. New York: Dover, 1991. p.94
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413:great stellated dodecahedron
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315:small stellated dodecahedron
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763:Shapes, Space, and Symmetry
371:regular polyhedral compound
61:, without creating any new
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755:(2006), pp. 253–261.
744:(1974), pp. 548–552.
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363:Kepler–Poinsot polyhedron
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749:The mathematical gazette
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646:Kepler–Poinsot polyhedra
373:. The uniform stars and
288:Kepler–Poinsot polyhedra
801:Glossary for Hyperspace
734:(1858), pp. 79–82.
580:(giving the shape of a
109:For example, a regular
739:Acta crystallographica
433:Excavated dodecahedron
383:excavated dodecahedron
375:compound of five cubes
367:uniform star polyhedra
21:Facet (disambiguation)
586:pentakis dodecahedron
640:derived the regular
19:For other uses, see
807:on 4 February 2007.
795:Olshevsky, George.
606:published his book
588:in Jamnitzer's book
377:are constructed by
284:regular icosahedron
778:Weisstein, Eric W.
648:) by faceting the
582:great dodecahedron
490:Regular compounds
310:great dodecahedron
117:, and the regular
78:faceted polyhedron
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401:Vertex-transitive
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320:great icosahedron
278:Faceted polyhedra
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803:. Archived from
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630:Stella octangula
621:regular compound
604:Wenzel Jamnitzer
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70:face diagonals
45:(also spelled
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576:Facetings of
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99:dual polytope
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724:Bertrand, J.
718:Bibliography
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671:dodecahedron
660:dodecahedron
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619:described a
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496:dodecahedron
408:dodecahedron
369:, and three
359:dodecahedron
357:The regular
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72:or internal
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759:Alan Holden
656:icosahedron
578:icosahedron
305:icosahedron
87:process to
816:Categories
797:"Faceting"
781:"Faceting"
690:References
625:tetrahedra
596:stellation
506:five cubes
90:stellation
55:polyhedron
832:Polytopes
822:Polyhedra
786:MathWorld
636:In 1858,
615:In 1619,
168:Pentagram
115:pentagram
47:facetting
827:Polygons
638:Bertrand
602:In 1568
365:, three
194:Compound
189:Compound
183:Decagram
177:Compound
128:Pentagon
111:pentagon
63:vertices
59:polytope
43:faceting
39:geometry
681:to the
667:regular
650:regular
623:of two
549:History
487:Convex
391:Convex
296:Convex
196:2{5/2}
186:{10/3}
138:Decagon
133:Hexagon
119:hexagon
51:polygon
653:convex
617:Kepler
584:) and
381:. The
171:{5/2}
695:Notes
191:2{5}
179:2{3}
679:dual
658:and
282:The
85:dual
76:. A
742:A30
65:.
57:or
37:In
818::
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761:,
753:90
751:,
732:46
730:,
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23:.
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