constructing a genus 2 surface from 8-gon

Here are two visualizations. ${}{}{}{}{}{}{}{}{}{}$

two ways of making a genus-two surface from an octogon

Here's a third, from Steve D's comment: third way


You can find this too on p. 301 of Hilbert & Cohn-Vossen "Geometry and the Imagination."

enter image description here

Tags:

Reference Request

Algebraic Topology

Related

Are there an infinite number of minibrots on the real line? Example of a set $Y$ that has zero Lebesgue measure and a continuous function $f$ such that $f(Y)$ is not a set of zero Lebesgue measure. When will $AB=BA$? Prime Numbers And Perfect Squares How many 3-digit positive integers are odd and do not contain digit 5? Explain a surprisingly simple optimization result Is the zero matrix the only symmetric, nilpotent matrix with real values? Prove that if 33 rooks are placed on a chessboard, at least five don't attack one another If $(ab)^3=a^3 b^3$, prove that the group $G$ is abelian. Is there another simpler method to solve this elementary school math problem? Can we simplify $\int_0^{\pi}\left(\frac{\sin nx}{\sin x}\right)^mdx$? Decipher the greeting card $( X^2 +Y^2 -1 ) ^3 - X^2 Y^3 = 0$

Recent Posts