Triangular pyramid
In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral face. It is a conic solid with polygonal base. A pyramid with an n-sided base has n + 1 vertices, n + 1 faces, and 2n edges. All pyramids are self-dual.
A right pyramid has its apex directly above the centroid of its base. Nonright pyramids are called oblique pyramids. A regular pyramid has a regular polygon base and is usually implied to be a right pyramid.
When unspecified, a pyramid is usually assumed to be a regular square pyramid, like the physical pyramid structures. A triangle-based pyramid is more often called a tetrahedron.
Among oblique pyramids, like acute and obtuse triangles, a pyramid can be called acute if its apex is above the interior of the base and obtuse if its apex is above the exterior of the base. A right-angled pyramid has its apex above an edge or vertex of the base. In a tetrahedron these qualifiers change based on which face is considered the base.
Pyramids are a subclass of the prismatoids. Pyramids can be doubled into bipyramids by adding a second offset point on the other side of the base plane.
A right pyramid with a regular base has isosceles triangle sides, with symmetry is Cnv or [1,n], with order 2n. It can be given an extended Schläfli symbol ( ) ∨ {n}, representing a point, ( ), joined (orthogonally offset) to a regular polygon, {n}. A join operation creates a new edge between all pairs of vertices of the two joined figures.
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