Simplicial complex - Revision history

Vipul: 3 revisions

2008-05-11T19:58:16Z

3 revisions

← Older revision	Revision as of 19:58, 11 May 2008
(No difference)

Vipul at 01:46, 22 May 2007

2007-05-22T01:46:17Z

← Older revision		Revision as of 01:46, 22 May 2007
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	* For any two simplices in the complex, either they do not intersect, or their intersection is a common face of both.		* For any two simplices in the complex, either they do not intersect, or their intersection is a common face of both.

	Here a '''simplex''' is a finite affine independent subset of the Euclidean space, and a '''face''' of a simplex is simply a subset of it. The elements of the subset are often called the '''vertices''' of the simplex, and a simplex of size <math>k+1</math> is termed a <math>k</math>-simplex.		Here a '''simplex''' is the set of all convex combinations of a finite affine independent subset of the Euclidean space, and a '''face''' of a simplex is simply a subset of it. The elements of the subset are often called the '''vertices''' of the simplex, and a simplex of size <math>k+1</math> is termed a <math>k</math>-simplex.

	The '''underlying space''' of a simplicial complex is defined as the union of all its simplices. A space that can be expressed as the underlying space of a simplicial complex is termed a [[polyhedron]], and such an expression i s termed a [[triangulation]].		The '''underlying space''' of a simplicial complex is defined as the union of all its simplices. A space that can be expressed as the underlying space of a simplicial complex is termed a [[polyhedron]], and such an expression i s termed a [[triangulation]].

Vipul: /* Definition */

2007-05-22T01:36:51Z

Definition

← Older revision		Revision as of 01:36, 22 May 2007
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	* For any two simplices in the complex, either they do not intersect, or their intersection is a common face of both.		* For any two simplices in the complex, either they do not intersect, or their intersection is a common face of both.

	Here a '''simplex''' is a finite affine independent subset of the Euclidean space, and a '''face''' of a simplex is simply a subset of it. The elements of the subset are often called the '''vertices''' of the simplex, and a simplex of size <math>k+1</math? is termed a <math>k</math>-simplex.		Here a '''simplex''' is a finite affine independent subset of the Euclidean space, and a '''face''' of a simplex is simply a subset of it. The elements of the subset are often called the '''vertices''' of the simplex, and a simplex of size <math>k+1</math> is termed a <math>k</math>-simplex.

	The '''underlying space''' of a simplicial complex is defined as the union of all its simplices. A space that can be expressed as the underlying space of a simplicial complex is termed a [[polyhedron]], and such an expression i s termed a [[triangulation]].		The '''underlying space''' of a simplicial complex is defined as the union of all its simplices. A space that can be expressed as the underlying space of a simplicial complex is termed a [[polyhedron]], and such an expression i s termed a [[triangulation]].

Vipul at 01:36, 22 May 2007

2007-05-22T01:36:35Z

New page

==Definition==

A (finite) simplicial complex is a finite collection of simplies in some Euclidean space such that:

* If any simplex belongs to the complex, so do all its faces
* For any two simplices in the complex, either they do not intersect, or their intersection is a common face of both.

Here a '''simplex''' is a finite affine independent subset of the Euclidean space, and a '''face''' of a simplex is simply a subset of it. The elements of the subset are often called the '''vertices''' of the simplex, and a simplex of size <math>k+1</math? is termed a <math>k</math>-simplex.

The '''underlying space''' of a simplicial complex is defined as the union of all its simplices. A space that can be expressed as the underlying space of a simplicial complex is termed a [[polyhedron]], and such an expression i s termed a [[triangulation]].