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Home > 2014 Mathematical Art Exhibition
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"View of the platycosm -a2, decorated with AMS, " by Charles Gunn (Technisches Universit├Ąt Berlin, Germany)

18" x 18", print of computer image, 2013

"I enjoy exploring two- and three-dimensional tessellations -- euclidean, spherical and hyperbolic, especially the "insider's" view of such spaces. I have been experimenting recently with alternative perspective rendering based on a spherical canvas surrounding the viewer. "

This is an insider's view of the platycosm -a2. ("Platycosm" is John Conway's term for a compact euclidean 3-manifold.) This platycosm is generated by a translation, a glide reflection and a screw motion with order-2 rotational part, in three mutually perpendicular directions. The fundamental domain is a cube, whose edges are rendered via the textured beams. The "geometry" consists of the initials AMS, in honor of one of the hosting orgranizations of the art show. The image is rendered conformally from the viewable sphere of an insider positioned in the scene. I sometimes call this "six-point perspective" rendering since one may see vanishing points not just in the x,y, and z directions but also in the -x, -y, and -z directions. --- Charles Gunn (

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American Mathematical Society