Decorative Knot Patterns

Lindsay D. Taylor

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A proof is given that, with the only exception of (3,2), all toroidal knots in R3 obtained in the standard way by stereographic projection of knots in S3 have tritangent planes.

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Let V be a two-dimensional real symmetric space with unit ball having 8n extreme points. Let λ(V) denote the absolute projection constant of V. We show that $λ (V) \leq λ (V_{n})$ where $V_{n}$ is the space whose ball is a regular 8n-polygon. Also we reprove a result of [1] and [5] which states that $4 / π = λ (l ₂^{(2)}) \geq λ (V)$ for any two-dimensional real symmetric space V.