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A hexagonal pyramid has seven vertices, twelve edges, and seven faces. One of its faces is hexagon, a base of the pyramid; six others are triangles. Six of the edges make up the pentagon by connecting its six vertices, and the other six edges are known as the lateral edges of the pyramid, meeting at the seventh vertex called the apex.
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The base regularity of a pyramid's base may be classified based on the type of polygon: one example is the star pyramid in which its base is the regular star polygon. [24] The truncated pyramid is a pyramid cut off by a plane; if the truncation plane is parallel to the base of a pyramid, it is called a frustum.
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A heptahedron can take a large number of different basic forms, or topologies. The most familiar are the hexagonal pyramid and the pentagonal prism. Also notable is the tetrahemihexahedron, which can be seen as a tessellation of the real projective plane. No heptahedra are regular.
The hexagonal bipyramid has a plane of symmetry (which is horizontal in the figure to the right) where the bases of the two pyramids are joined. This plane is a regular hexagon. There are also six planes of symmetry crossing through the two apices. These planes are rhombic and lie at 30° angles to each other, perpendicular to the horizontal plane.
In geometry, the gyroelongated pyramids (also called augmented antiprisms) are an infinite set of polyhedra, constructed by adjoining an n-gonal pyramid to an n-gonal antiprism. There are two gyroelongated pyramids that are Johnson solids made from regular triangles and square, and pentagons.