# Yana Mohanty and Bjoern Muetzel

Inventor / Educator / Mathematician; Lecturer in Mathematics
Imathgination LLC; Department of Mathematics, Dartmouth College
San Diego, California, USA; Hanover, New Hampshire, USA

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 helps me find novel ways to look at classical mathematical structures. The digital nature of the artwork allows long distance collaboration with other artists, further enriching the creative experience.

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.

The Right Rose
30 x 30 cm
Photography
2019

The snub dodecahedron is one of two chiral Archimedean solids. At 92 faces, it is a fairly good approximation of a sphere, but its chirality is not easy to see. This made the snub dodecahedron an ideal subject for a photograph by a spherical camera. An unusual presentation of the snub dodecahedron, “The Right Rose” resulted from placing the spherical camera close to the center of the solid, and stereographically projecting from the “pole” opposite to where the camera is inserted. The edges of the snub dodecahedron are roughly mapped to arcs of circles on the plane, which look like petals tangent to the boundary of the image. Unlike the medieval rose windows, this rose is right—in the chiral sense!

Lost in Reflection
27 x 27 x 27 cm
Mirrors attached to plastic tiles
2019

Our goal in this project was to highlight the chirality of the snub dodecahedron. This property is immediately evident in the colorings of the solid we have seen. We divided the solid into two congruent hemispheres, with each hemisphere consisting of a pentagon surrounded by a multi-colored spiral. When seen from above either pole, the spiral curves counter clockwise. However, the orders of sequences of colors at the two poles are reversed. This reversal is a necessary condition for 5-coloring the solid while keeping the sequences of colors the same. On the inside a psychedelic mirror landscape reveals itself whose fractal geometry is reminiscent of the view into hyperbolic 3-manifolds.