Triangle (EntityTopic, 17)
From Hi.gher. Space
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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, 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 == | |
| - | + | ||
*The area of an '''arbitrary''' triangle is: | *The area of an '''arbitrary''' triangle is: | ||
<blockquote>''ab''sin(''C'')2<sup>-1</sup></blockquote> | <blockquote>''ab''sin(''C'')2<sup>-1</sup></blockquote> | ||
Revision as of 11:17, 22 September 2007
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, 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%)
- Snub dodecahedron (80×, 87%)
- Snub cube (32×, 84%)
- Square pyramid (4×, 80%)
- Truncated dodecahedron (20×, 63%)
- Cuboctahedron (8×, 57%)
- Truncated cube (8×, 57%)
- Truncated tetrahedron (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 |
