Details

This Demonstration describes all kaleidoscopes from [1, pp. 155–161] that are not covered in our previous Demonstrations.

The kaleidoscopes based on open triangular prisms have triangular horizontal cross sections with angles , , , where , , are positive integers. The solutions of the equation are , , . Varying a point in the triangle gives the vertices of certain isogonal tessellations [1, p. 157].

Tetrahedral kaleidoscopes are constructed as certain cross sections of a rectangular block of dimensions [1, p. 159].

Five mirrors can be arranged in the form of certain triangular prisms and lead to solid tessellations of prisms [1, p. 160].

Six mirrors are arranged as the sides of a rectangular prism to give a solid tessellation of rectangular blocks [1, p. 161].

Reference

[1] W. W. R. Ball and H. S. M. Coxeter, Mathematical Recreations and Essays, 13th ed., New York: Dover Publications, 1987.