Triangle (EntityTopic, 17)
From Hi.gher. Space
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<blockquote><sup>1</sup>∕<sub>2</sub> · ''ab'' · sin ''C''</blockquote> | <blockquote><sup>1</sup>∕<sub>2</sub> · ''ab'' · sin ''C''</blockquote> | ||
| - | == | + | == Dissection == |
| - | The equilateral triangle of side 1 may be [[ | + | The equilateral triangle of side 1 may be [[dissect]]ed into 3× triangle with sides 1, 2×3<sup>-2<sup>-1</sup></sup> and angles 2×30°, 120°. |
== Use == | == Use == | ||
Revision as of 15:09, 21 November 2011
A triangle is a two-dimensional simplex.
Equations
- The area of an equilateral triangle with side length l is:
√3∕4 · l2
- The area of an arbitrary triangle, where a and b are two sides of the triangle and C is the angle between them, is:
1∕2 · ab · sin C
Dissection
The equilateral triangle of side 1 may be dissected 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×)
| Simplices |
| triangle • tetrahedron • pyrochoron • pyroteron • pyropeton |
| Notable Dishapes | |
| Flat: | triangle • square • pentagon • hexagon • octagon • decagon |
| Curved: | circle |
| 3. 11 Square | 4. 11 Triangle | 5. 3 Sphere |
| List of tapertopes | ||
