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A right pyramid is a pyramid whose base is circumscribed about a circle and the altitude of the pyramid meets the base at the circle's center; otherwise, it is oblique. [12] This pyramid may be classified based on the regularity of its bases. A pyramid with a regular polygon as the base is called a regular pyramid. [13]
Its vertex–center–vertex angle—the angle between lines from the tetrahedron center to any two vertices—is = (), denoted the tetrahedral angle. [9] It is the angle between Plateau borders at a vertex. Its value in radians is the length of the circular arc on the unit sphere resulting from centrally projecting one edge of the ...
The solid angle of a four-sided right rectangular pyramid with apex angles a and b (dihedral angles measured to the opposite side faces of the pyramid) is = ( ()). If both the side lengths ( α and β ) of the base of the pyramid and the distance ( d ) from the center of the base rectangle to the apex of the pyramid (the center of ...
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]
Square (regular quadrilateral): all four sides are of equal length (equilateral), and all four angles are right angles. An equivalent condition is that opposite sides are parallel (a square is a parallelogram), and that the diagonals perpendicularly bisect each other and are of equal length.
In a triangle, any arbitrary side can be considered the base. The two endpoints of the base are called base vertices and the corresponding angles are called base angles. The third vertex opposite the base is called the apex. The extended base of a triangle (a particular case of an extended side) is the line that contains the base.
A square pyramid has five vertices, eight edges, and five faces. One face, called the base of the pyramid, is a square; the four other faces are triangles. [2] Four of the edges make up the square by connecting its four vertices. The other four edges are known as the lateral edges of the pyramid; they meet at the fifth vertex, called the apex. [3]
The triangle is the 2-simplex, a simple shape that requires two dimensions. Consider a triangle ABC , a shape in a 2-dimensional space (the plane in which the triangle resides). One can place a new point D somewhere off the plane.