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In geometry, a **Blind polytope** is a convex polytope composed of regular polytope facets.
The category was named after the German couple Gerd and Roswitha Blind, who described them in a series of papers beginning in 1979.^{[1]}
It generalizes the set of semiregular polyhedra and Johnson solids to higher dimensions.^{[2]}

The set of convex uniform 4-polytopes (also called semiregular 4-polytopes) are completely known cases, nearly all grouped by their Wythoff constructions, sharing symmetries of the convex regular 4-polytopes and prismatic forms.

Set of convex uniform 5-polytopes, uniform 6-polytopes, uniform 7-polytopes, etc are largely enumerated as Wythoff constructions, but not known to be complete.

Pyramidal forms: (4D)

- (
*Tetrahedral pyramid*, ( ) ∨ {3,3}, a tetrahedron base, and 4 tetrahedral sides, a lower symmetry name of regular 5-cell.) - Octahedral pyramid, ( ) ∨ {3,4}, an octahedron base, and 8 tetrahedra sides meeting at an apex.
- Icosahedral pyramid, ( ) ∨ {3,5}, an icosahedron base, and 20 tetrahedra sides.

Bipyramid forms: (4D)

- 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]}

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.

For example, a cubic bipyramid has 12 square pyramid cells.

**^**Blind, R. (1979), "Konvexe Polytope mit kongruenten regulären -Seiten im ( )",*Commentarii Mathematici Helvetici*(in German),**54**(2): 304–308, doi:10.1007/BF02566273, MR 0535060, S2CID 121754486**^**Klitzing, Richard, "Johnson solids, Blind polytopes, and CRFs",*Polytopes*, retrieved 2022-11-14**^**"aurap".*bendwavy.org*. Retrieved 10 April 2023.**^**"Johnson solids et al".*bendwavy.org*. Retrieved 10 April 2023.

- Blind, Roswitha (1979). "Konvexe Polytope mit regulären Facetten im
**R**^{n}(n≥4)" [Convex polytopes with regular facets in**R**^{n}(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
**R**^{4}, bei denen alle Facetten reguläre Tetraeder sind" [All convex polytopes in**R**^{4}, the facets of which are regular tetrahedra].*Monatshefte für Mathematik*(in German).**89**(2): 87–93. doi:10.1007/BF01476586. S2CID 117654776. - 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. S2CID 118720486. - Blind, Gerd; Blind, Roswitha (1991). "The semiregular polytopes".
*Commentarii Mathematici Helvetici*.**66**: 150–154. doi:10.1007/BF02566640. S2CID 119695696.

- Blind polytope
- Convex regular-faced polytopes