Growing Shapes: Unfolding simple quadrangulations of the sphere one quad at a time
James Mallos

Hyperseeing: Proceedings of Shape Creation Using Layouts, Programs, & Technology (SCULPT) 2023
Pages 39–44
Regular Papers

Abstract

The object of this research is making sculpture that grows, that is, not merely changing in shape, but developing, one small step at a time, from small to large, maintaining definite, reproducible shape all the while. Recent advances in graph theory have shown that the simple quadrangulations of the sphere can be generated inductively by a set of map operations more restricted in their context of application than sets previously known. I show that this new pair of operations can be realized by local unfolding of quads that have been hinged along both diagonals. Current development of these ideas is demonstrated in a small hinged-plate model that grows from 2 quads to 6 quads.

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