Triangle (EntityTopic, 17)
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== Equations == | == Equations == | ||
- | *The area of an '''arbitrary''' triangle is: | + | *The area of an equilateral triangle with side length ''l'' is: |
+ | <blockquote>''l''<sup>2</sup>[[Sine values|S<sub>4</sub>]]</blockquote> | ||
+ | *The area of an arbitrary triangle, where ''a'' and ''b'' are two sides of the triangle and ''C'' is the angle between them, is: | ||
<blockquote>''ab''sin(''C'')2<sup>-1</sup></blockquote> | <blockquote>''ab''sin(''C'')2<sup>-1</sup></blockquote> | ||
- | |||
== Segmentation == | == Segmentation == |
Revision as of 10:22, 11 March 2011
A triangle is a two-dimensional simplex.
Equations
- The area of an equilateral triangle with side length l is:
l2S4
- The area of an arbitrary triangle, where a and b are two sides of the triangle and C is the angle between them, is:
absin(C)2-1
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×)
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 |