Summary: Geometry and the Imagination
An academic exercise presented in partial fulfillment for the degree of
Bachelor of Science with Honours in Applied Mathematics.
Supervisor: Associate Professor Helmer Aslaksen
Department of Mathematics
National University of Singapore
I would like to thank my supervisor, A/P Aslaksen, for conducting this wonderful
project. I am grateful to him for his time and his patience with me. I benefit greatly from
discussions I have had with him on this project, and I hereby express my appreciation
for his guidance full of inspirations. This project has been a meaningful and pleasant
experience with excitements and joys of discoveries, which I will always remember.
I would like to dedicate the regular octahedron shown below to my lovely girlfriend,
Goose. To me, she is as nice and perfect as a regular octahedron.
I would like to dedicate the space hexagon highlighted in bold on the regular octahedron
to all the people who have been kind to me. I would like to share my joys with you all.
I would like to dedicate the hyperboloid of one sheet that contains all six sides of the