# Non-Spherical Geodesic Structures

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

In a 1991 Graphics Gallery of the Mathematica Journal [1], we demonstrated a system for building "Many-Handled Surfaces" modeled after chemical molecular bonding geometry. Here is an interactive version.

Contributed by: Stewart Dickson (January 2023)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

"Geodesation" of the tetrahedron suggests non-spherical many-handled surfaces based on the geometry of carbon bonds in organic chemistry. Here we present structures modeled after the linear alkanes (methane to decane ) and the fused-ring structure adamantane ), based on cyclohexanes.

Geodesation of the octahedron suggests a hexavalent bonding geometry similar to iron. The surface subdivision method of the octahedron we use here closely approximates the infinite Schwartz triply periodic minimal surface.

The original 1991 notebook [1] demonstrated geodetation of the wireframes of the bonding units and orientation of the hemispherical end caps.

Here, given a pre-constructed list of transforms representing the molecular skeleton, we automatically determine where hemispherical end caps can be placed.

References

[1] S. Dickson, Graphics Gallery: "Many-Handled Surfaces," *The Mathematica Journal*, 1(4), 1991 pp. 51–58.

[2] Rosso, S. et al., "Modeling Symmetric Minimal Surfaces by Mesh Subdivision," L. Roucoules, M. Paredes, B. Eynard, P. Morer Camo, and C. Rizzi (eds.) *Advances on Mechanics, Design Engineering and Manufacturing III,* JCM 2020. Lecture Notes in Mechanical Engineering, Springer: Cham. https://doi.org/10.1007/978-3-030-70566-4_ 40.

## Permanent Citation