# Carlo Séquin

Professor of Computer Science

University of California, Berkeley

Berkeley, CA, USA

My inspiration for this work comes from an 18-inch sand-cast by Charles O. Perry, which he called "Star Cinder." This is a single-sided, soapfilm-like surface, suspended by an "Orderly Tangle" of ten triangular equatorial loops that are interlinked with icosahedral symmetry. The surface shell is confined to the outer 20% of the spherical volume of this sculpture. I am now focused on making more volume-filling versions of such surfaces, comprising multiple nested shells that are also linked in the radial directions. Furthermore, I am exploring to what extent such "Space-Shells" can be be constructed using surfaces of higher genus.

Spherical, 3-Level "Space-Shell" based on the Cuboctahedron

18 x 18 x 18 cm

ABS, 3D-print

2019

The design of this 3-level "Space-Shell" starts with the cuboctahedron and its dual, the rhombic dodecahedron. The edges of these semi-regular solids are represented by twisted ribbon segments that twist through 180 degrees between two adjacent vertices. With proper concentric alignment, the mid-edge points of the two dual shells, where the twisted ribbons have tangent components pointing towards the center of the sphere, will align in the radial directions. At these edge-crossing locations, an additional ribbon twisting through 90 degrees can link adjacent nested shells in the radial direction. In this particular "Space-Shell" two cuboctahedral shells are separated by an interspersed rhombic dodecahedral shell.

"Ring-World" -- a 3-Level Toroidal "Space-Shell"

22 x 22 x 10 cm

ABS, 3D-print

2019

The basic approach to creating multi-level "Space-Shells" introduced in the spherical sculpture shown first is quite versatile and can readily be applied to toroidal structures as well. The quadrilateral tiling used on the torus is its own dual; thus similar shells can readily be nested. However, for any spherical "Space-Shells" just the two dual ribbon meshes needed to be designed, which then can be instantiated multiple times using simple uniform scaling. In a toroidal structure every nested shell has a different geometry and needs to be designed individually. The "Ring-World" model took 76 hours to print on a Stratasys Dimension 1200 machine and 48 hours in a lie bath to remove the internal support.