geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

, the heptagonal antiprism is the fifth in an infinite set of

antiprisms In geometry, an antiprism or is a polyhedron composed of two parallel direct copies (not mirror images) of an polygon, connected by an alternating band of triangles. They are represented by the Conway notation . Antiprisms are a subclass ...

formed by two parallel polygons separated by a strip of triangles. In the case of the heptagonal antiprism, the caps are two regular

heptagon In geometry, a heptagon or septagon is a seven-sided polygon or 7-gon. The heptagon is sometimes referred to as the septagon, using ''Wikt:septa-, septa-'' (an elision of ''Wikt:septua-, septua-''), a Latin-derived numerical prefix, rather than ...

s. As a result, this polyhedron has 14 vertices, and 14 equilateral triangle faces. There are 14 edges where a triangle meets a heptagon, and another 14 edges where two triangles meet. The heptagonal antiprism was first depicted by

Johannes Kepler Johannes Kepler (27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, Natural philosophy, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best know ...

, as an example of the general construction of antiprisms. See als
illustration A
of a heptagonal antiprism.

References

Prismatoid polyhedra {{Polyhedron-stub