Triangle (EntityTopic, 17)
From Hi.gher. Space
(Difference between revisions)
m (add SSC3) |
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| ssc=G3 | | ssc=G3 | ||
| ssc2=G3 | | ssc2=G3 | ||
| - | |||
| pv_circle=<sup>[[Sine values|S<sub>4</sub>]]</sup>⁄<sub>π</sub> ≈ 0.2757 | | pv_circle=<sup>[[Sine values|S<sub>4</sub>]]</sup>⁄<sub>π</sub> ≈ 0.2757 | ||
| pv_square=[[Sine values|S<sub>1</sub>]]+S<sub>1</sub><sup>3</sup>S<sub>5</sub><sup>-2</sup> ≈ 0.2774 | | pv_square=[[Sine values|S<sub>1</sub>]]+S<sub>1</sub><sup>3</sup>S<sub>5</sub><sup>-2</sup> ≈ 0.2774 | ||
Revision as of 16:34, 22 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 | ||
