Streptohedron and Trapezohedron

Take an

n

-sided regular pyramid and form the union with its mirror image with respect to its base plane to get an

n

-gonal bipyramid. Its faces are mutually congruent isosceles triangles. (With properly chosen height and

n

=4 you get the regular octahedron as a special case.)

Rotating its upper and lower parts by

360/2n

degrees yields a type of polyhedron called a streptohedron. Its faces are mutually congruent kites. It is also called a deltohedron or a trapezohedron.

In contrast to trapezohedra, which exhibit only rotational symmetry, both streptohedra and bipyramids also have planes of symmetry that pass through their

n

-fold axes (here only the axes of rotation are shown to avoid crowding).