A Grünbaum Polyhedron in Antiprism
25 Aug 2018
A paper from 2012, The Regular Grünbaum Polyhedron of Genus 5, includes a polyhedron of genus 5, earlier discovered by Grünbaum, that is an embedding of the {3,8} Fricke-Klein regular map. The polyhedron (Figure 2 and 3) can be recreated using the wythoff program in Antiprism, although the exact proportions are a little different in the paper.
wythoff -p [3VE2F]0EV,0fe0EV0fevfV,0F,0V0F0evfe oct
The polyhedron in Figure 4 can be created with a small change:
wythoff -p [3VE2F]0EV,0fe0EV0fevfV,0F,0V0E0F oct
These can also be used to generate the genus 11 polyhedra in Figure 5: just replace oct with ico.
Here’s the titular Grünbaum polyhedron of genus 5:
Related Posts
- 2023-11-04: Spherical area coordinates, and a derived triangle center
- 2023-07-29: Homogeneous coordinates on the sphere with vectors
- 2022-08-30: Scaling the Schwarz triangle function
- 2022-08-27: Edges in the image of the Schwarz triangle function
- 2022-07-20: Area-preserving swirling of the disk
- 2022-03-03: Some dubious ways to calculate conformal polyhedral projections
- 2021-10-02: A variation on the Chamberlin trimetric map projection
- 2021-08-31: Snyder's equal-area projection
- 2021-06-12: Perspective projections with vectors
- 2021-05-29: A (sort of) Euclidean triangle on a non-Euclidean surface