Triangle (EntityTopic, 17)
From Hi.gher. Space
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}}{{STS Uniform polytope | }}{{STS Uniform polytope | ||
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A '''triangle''' is a two-dimensional [[simplex]]. | A '''triangle''' is a two-dimensional [[simplex]]. | ||
- | The triangle is important as all [[polygon]]s can be defined as the [[union]] of a [[set]] of triangles, and all [[polytope]]s in greater than two dimensions can be defined as the [[hypervolume]] bounded by the union of a set of triangles. | + | The triangle is important as all [[polygon]]s can be defined as the [[union]] of a [[set]] of triangles joined edge to edge, and all [[polytope]]s in greater than two dimensions can be defined as the [[hypervolume]] bounded by the union of a set of triangles. |
== Equations == | == Equations == |
Revision as of 22:45, 5 November 2008
A triangle is a two-dimensional simplex.
The triangle is important as all polygons can be defined as the union of a set of triangles joined edge to edge, and all polytopes in greater than two dimensions can be defined as the hypervolume bounded by the union of a set of triangles.
Equations
- The area of an arbitrary triangle is:
absin(C)2-1
- where a and b are two sides of the triangle and C is the angle between them.
Segmentation
The equilateral triangle of side 1 may be segmented into 3× triangle with sides 1, 2×3-2-1 and angles 2×30°, 120°.
Use
Triangular faces are found in these trishapes on FGwiki:
- Icosahedron (20×, 100%)
- Octahedron (8×, 100%)
- Tetrahedron (4×, 100%)
- Dodecahedral snub (80×, 87%)
- Cubic snub (32×, 84%)
- Square pyramid (4×, 80%)
- Icosidodecahedron (20×, 63%)
- Dodecahedral truncate (20×, 63%)
- Cuboctahedron (8×, 57%)
- Cubic truncate (8×, 57%)
- Tetrahedral truncate (4×, 50%)
- Triangular prism (2×, 40%)
Triangular segments are found in these dishapes on FGwiki:
- Hexagon (6×)
Notable Dishapes | |
Flat: | triangle • square • pentagon • hexagon • octagon • decagon |
Curved: | circle |