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Simplex K-3-C Red Arrow; Simplex K-2-S Red Arrow; Simplex W-2-S Red Arrow; Simplex R-2-D Red Arrow Dual Plane a.k.a. Simplex Racer; Simplex S-2 Kite [4] Simplex ...
Simplex K-2-C Red Arrow 2 seat enclosed cabin. Together, about 10 K-2s were built. Simplex K-3-C Red Arrow 3 seat enclosed cabin. Simplex W-2-S Warner Scarab engine, heavily revised undercarriage and wing struttage. About 10 built, though one was a K-2-S conversion. Simplex R-2-D Red Arrow Dual Plane or Simplex Racer
The standard simplex or probability simplex [2] is the (k − 1)-dimensional simplex whose vertices are the k standard unit vectors in , or in other words {: + + =, =, …,}. In topology and combinatorics , it is common to "glue together" simplices to form a simplicial complex .
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For a single simplex s, the star of s is the set of simplices in K that have s as a face. The star of S is generally not a simplicial complex itself, so some authors define the closed star of S (denoted S t S {\displaystyle \mathrm {St} \ S} ) as C l s t S {\displaystyle \mathrm {Cl} \ \mathrm {st} \ S} the closure of the star of S.
A key concept in defining simplicial homology is the notion of an orientation of a simplex. By definition, an orientation of a k-simplex is given by an ordering of the vertices, written as (v 0,...,v k), with the rule that two orderings define the same orientation if and only if they differ by an even permutation.
Let K be a geometric simplicial complex (GSC). A subdivision of K is a GSC L such that: [1]: 15 [2]: 3 |K| = |L|, that is, the union of simplices in K equals the union of simplices in L (they cover the same region in space). each simplex of L is contained in some simplex of K.
Let K and L be two geometric simplicial complexes (GSC). A simplicial map of K into L is a function : such that the images of the vertices of a simplex in K span a simplex in L. That is, for any simplex , ((())).