Tetrahedral bipyramid, { } + {3,3}, a tetrahedron center, and 8 tetrahedral cells on two side.
(Octahedral bipyramid, { } + {3,4}, an octahedron center, and 8 tetrahedral cells on two side, a lower symmetry name of regular
16-cell.)
Icosahedral bipyramid, { } + {3,5}, an icosahedron center, and 40 tetrahedral cells on two sides.
Augmented forms: (4D)
Rectified 5-cell augmented with one
octahedral pyramid, adding one vertex for 13 total. It retains 5 tetrahedral cells, reduced to 4 octahedral cells and adds 8 new tetrahedral cells.[3]
Convex Regular-Faced Polytopes
Blind polytopes are a subset of convex regular-faced polytopes (CRF).[4]
This much larger set allows CRF 4-polytopes to have
Johnson solids as cells, as well as regular and semiregular polyhedral cells.
Blind, Roswitha (1979). "Konvexe Polytope mit regulären Facetten im Rn (n≥4)" [Convex polytopes with regular facets in Rn (n≥4)]. In Tölke, Jürgen; Wills, Jörg. M. (eds.). Contributions to Geometry: Proceedings of the Geometry-Symposium held in Siegen June 28, 1978 to July 1, 1978 (in German). Birkhäuser, Basel. pp. 248–254.
doi:
10.1007/978-3-0348-5765-9_10.{{
cite book}}: CS1 maint: location missing publisher (
link)
Blind, Gerd; Blind, Roswitha (1980). "Die konvexen Polytope im R4, bei denen alle Facetten reguläre Tetraeder sind" [All convex polytopes in R4, the facets of which are regular tetrahedra]. Monatshefte für Mathematik (in German). 89 (2): 87–93.
doi:
10.1007/BF01476586.
S2CID117654776.
Blind, Gerd; Blind, Roswitha (1989). "Über die Symmetriegruppen von regulärseitigen Polytopen" [On the symmetry groups of regular-faced polytopes]. Monatshefte für Mathematik (in German). 108 (2–3): 103–114.
doi:
10.1007/BF01308665.
S2CID118720486.