# Yana Mohanty and Bjoern Muetzel

Yana Mohanty: I got a spherical camera for my birthday three years ago, and my photography has never been the same. I found that the spherical camera allows me to build on other artists' work and, simultaneously, create an exercise in visualization for the viewer. This is my first collaboration on a spherical camera project with another mathematician.

Bjoern Muetzel: I am a mathematician working in the area of low dimensional geometry and topology. I have always been fascinated by the intersection of math and art and especially by the numerous beautiful patterns found in nature. To convey and disseminate this enchantment, I organize geometry activities for children in nearby schools using a variety of geometric shapes and tiles.

What happens when you attach mirror surfaces to the inside faces of a rhombicosidodecahedron? We set out to find this out by placing a spherical camera near the center of the solid and then stereographically projecting the output. In this image, the “pole” of the projection was the face opposite to the one through which the camera was placed. Each “petal” of the flower is the image of a decagon (formed by the boundary of a pentagon surrounded by triangles and squares) on the actual rhombicosidodecahedron, taken to almost circles by the stereographic projection. Careful placement of the camera allows us to see reflections of pentagons in other pentagons and squares.

Looking into the two Archimedean solids provides a view into a hypnotic mirror world that is reminiscent of the view into hyperbolic three manifolds.

When you attach mirror surfaces to the faces of a rhombicosidodecahedron, and you look inside, the result is mesmerizing. We wanted to explore the experience through the eye of a spherical camera placed near the center of the solid. The final image is approximately the stereographic projection from the “pole” through which the camera is placed. Careful placement of the camera allows us to see reflections of pentagons in other pentagons and squares.