Sphericon

Sphericon is a ruled surface, of zero Gaussian curvature, given by a parametrisation, immersed.

Open Sphericon in the interactive viewer →

aperiodic def-parametric flat immersed implemented ruled

Formula

x(u, v)

v \cos\left(u\right)

y(u, v)

v \sin\left(u\right)

z(u, v)

1 - v

Properties

Family: ruled
Given by: a parametrisation
Curvature: zero Gaussian curvature
Periodicity: not periodic
Ends: 0
Embedding: immersed
Fidelity: exact
Exactness: elementary

Sources

Chart as curated in tools/surfdb/charts.py, verified numerically against the curvature condition the record claims (measured over the chart by the validator and the charts self-test).

David Swart, "Arcs on Spheres and Snakes on Planes", Bridges 2024 (the sphericon = solid of revolution of a regular polygon, halved and its cross-section rotated onto itself).
I. Sabitov / P. Roberts (polysphericons); H-ITS Polysphericons project, https://www.h-its.org/projects/polysphericons/ .
Sphericon invented by Colin J. Roberts (Baldock, England); popularized by Ian Stewart, "Cone with a Twist", Mathematical
Recreations, Scientific American, October 1999. See also Wikipedia "sphericon".