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Concept
Square pyramid
Summary
In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it is a right square pyramid, and has C_4v symmetry. If all edge lengths are equal, it is an equilateral square pyramid, the Johnson solid J_1.
A possibly oblique square pyramid with base length l and perpendicular height h has volume:
In a right square pyramid, all the lateral edges have the same length, and the sides other than the base are congruent isosceles triangles.
A right square pyramid with base length l and height h has surface area and volume:
The lateral edge length is:
the slant height is:
The dihedral angles are:
between the base and a side:
between two sides:
If all edges have the same length, then the sides are equilateral triangles, and the pyramid is an equilateral square pyramid, Johnson solid J1.
The Johnson square pyramid can be characterized by a single edge length parameter l.
The height h (from the midpoint of the square to the apex), the surface area A (including all five faces), and the volume V of an equilateral square pyramid are:
The dihedral angles of an equilateral square pyramid are:
between the base and a side:
between two (adjacent) sides:
A square pyramid can be represented by the wheel graph W5.
Square pyramids fill space with tetrahedra, truncated cubes, or cuboctahedra.
The square pyramid is topologically a self-dual polyhedron. The dual's edge lengths are different due to the polar reciprocation.
Official source
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