Three-dimensional nets and polyhedra

In a storage room of the University of Minnesota, there used to be (and probably still are) four large isosceles triangular mirrors, with edges proportional to 2 : y/3 : y3 , relics of an abandoned film project. If they were put together as faces of an 'isosceles' tetrahedron (with some device to prevent the sloping mirrors from sagging under their own weight), and if you could look in through a hole in one of the edges, you would see a remarkable array of images. For this tetragonal disphenoid is one of the three kinds of tetrahedron that can serve as a fundamental region for a reflection group [Coxeter 1973, p. 84; Shubnikov and Koptsik 1974, p. 201]. It (or the group) is denoted by a 'Dynkin symbol'