3D Polyhedra

About this Course

About the Course

In this course, Professor Satyan Devadoss (University of San Diego) explores 3-dimensional polyhedra and objects in higher dimensions. In the first mini-lecture, we introduce 2-dimensional polygons, in particular regular polygons. In the second mini-lecture, we think about the construction of regular 3-dimensional polyhedra out of polygons, and consider the constraint that must be placed on the corner angles. In the third mini-lecture, we use our constraint equation from the previous mini-lecture to discover that there are only five regular polyhedra, known as the Platonic solids. In the fourth mini-lecture, we address how to express 4D objects in our 3D world by considering how to express 3D objects in a 2D world using the Shlegel diagram. Finally, in the fifth mini-lecture, we explore regular polytopes in 4D, 5D, and beyond.

About the Lecturer

Satyan Devadoss is the Fletcher Jones Chair of Applied Mathematics and Professor of Computer Science at the University of San Diego. His research interests are in topology and geometry, with inspiration coming from theoretical physics, phylogenetics, and scientific visualization. He was a professor of mathematics for 15 years at Williams College prior to arriving at the University of San Diego, and has held visiting positions at Ohio State, UC Berkeley, Mathematical Sciences Research Institute, Harvey Mudd, and Stanford.

Professor Devadoss is an inaugural fellow of the American Mathematical Society. He has been awarded three prestigious teaching wards by the Mathematical Association of America: (i) the Henry L Alder National Teaching Award in 2007, to honour young faculty whose teaching has influence beyond their own classrooms; (ii) the Northeastern Sectional Award for Distinguished Teaching in 2014, for teaching that has been extra ordinarily successful; (iii) and the Deborah and Franklin Tepper Haimo National Teaching Award in 2016, to honour teachers who have been widely recognised as extraordinarily successful.

Professor Devadoss is a coauthor of the textbook Discrete and Computational Geometry (2011), and a coauthor of the tradebook Mage Merlin's Unsolved Mathematical Mysteries (2020). In 2017, he led a team at the University of San Diego to receive a $1M grant from the Fletcher Jones Foundation for the renovation of the mathematics department. The centrepiece of this renovation is his Math Studio that serves as a laboratory promoting the physical experience surrounding mathematics research.