Triangle (EntityTopic, 17)

From Hi.gher. Space

Revision as of 22:23, 3 January 2012

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×)

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