For example:
An example of a genus 0 surface is a ball.
An example of a genus 1 surface is a doughnut.
An example of a genus 3 surface is a pretzel.

However, there is, to the best of my knowledge, no familiar object which describes a genus 2 surface. "Thickened out 8" just doesn't cut it.

Your mission, should you choose to accept it, is to tell me about a reasonably commonplace object of genus 2.