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The follow-up definition above may result in more precise properties. For example, since the perimeter of an isosceles triangle is the sum of its two legs and base, the equilateral triangle is formulated as three times its side. [3] [4] The internal angle of an equilateral triangle are equal, 60°. [5]
Triangles have many types based on the length of the sides and the angles. A triangle whose sides are all the same length is an equilateral triangle, [3] a triangle with two sides having the same length is an isosceles triangle, [4] [a] and a triangle with three different-length sides is a scalene triangle. [7]
The exterior face is a 60-90-30 triangle which is one-sixth of a tetrahedron face. The three faces interior to the tetrahedron are: a right triangle with edges , , , a right triangle with edges , , , and a right triangle with edges , , .
At each vertex of the solid, the total, among the adjacent faces, of the angles between their respective adjacent sides must be strictly less than 360°. The amount less than 360° is called an angle defect. Regular polygons of six or more sides have only angles of 120° or more, so the common face must be the triangle, square, or pentagon. For ...
The same shape is also known as a triangular dipyramid [1] [2] or trigonal bipyramid. [3] If these tetrahedra are regular, all faces of a triangular bipyramid are equilateral. It is an example of a deltahedron, composite polyhedron, and Johnson solid.
Triangular antiprisms: Two faces are equilateral, lie on parallel planes, and have a common axis of symmetry. The other six triangles are isosceles. The regular octahedron is a special case in which the six lateral triangles are also equilateral. Tetragonal bipyramids, in which at least one of the equatorial quadrilaterals lies on a plane. The ...
The dihedral angle between two adjacent square faces is the internal angle of an equilateral triangle π /3 = 60°, and that between a square and a triangle is π /2 = 90°. [7] The volume of any prism is the product of the area of the base and the distance between the two bases. [8]
A 3-simplex with triangular symmetry can be expressed as the join of an equilateral triangle and 1 point: 3.( )∨( ) or {3}∨( ). A regular tetrahedron is 4 ⋅ ( ) or {3,3} and so on. The numbers of faces in the above table are the same as in Pascal's triangle , without the left diagonal.