## Artists

## Statement

For several decades I have been exploring ways to turn mathematical models into small geometrical sculptures. Often, I start with a particularly intriguing sculpture by a recognized artist. For this exhibition I have been inspired by Tord Tengstrand’s “3-2-1”-sculpture. This small model gets its name from the fact that it has three edges, two vertices, but only a single, wildly branching-out, smoothly connected face, which connects to itself across the three edges. Here are two derivative designs that can be viewed as members of the same family.

## Artworks

For this model, I first construct a derivative Tengstrand “2-2-1”-sculpture with only two edges winding around the two prismatic branches that connect the two vertices. Half of that structure is an arched module with two legs.
Six such modules can readily be strung together to form a handle-body of genus-1 with an “up-down-up-down-up-down”-zigzag configuration above a hexagonal footprint, comprising six edges, six vertices, and just a single face. A more interesting sculpture results if the six arches are connected into an interlinked trefoil structure.

For this model, I enhance Tengstrand’s sculpture to a “4-2-1”-configuration. I use half of this as a pliable module in the shape of a 4-sided pyramid with four legs sticking out at the bottom. I bend these legs outward, so that opposite legs end up mutually perpendicular to each other. I then place six copies of this module at the corners of an octahedron and join the 24 legs to form the 12 edges of an octahedral frame structure. I maintain the helically twisting sharp-edge-curves as they were in Tord’s original. This leads to a satisfactory edge configuration that borders a single smoothly connected face.