MA-3329 Modern Geometry Name: ____________________________

Fun Paper Model Day #2

Recall Fun Paper Model Day #1. You removed angles from your papers to form pointy cones (elliptic points), and added angles to your papers to make 'ruffles' (hyperbolic points). The angles which are removed form an

angle deficit relative to the 360 degrees you would expect to find in a plane. Adding extra angles causes a

negative deficit. Today, we will split into groups and take turns with various paper models to find the total angle deficits for various simple closed 3D objects. The tetrahedron will be done up-front as an example for

you before you split into groups. Each object is color-coordinated with its flat pattern for your convenience.

name of object	notes for self	total angle deficit in degrees	deficit in radians
tetrahedron	made from 4 equilateral triangles, total of 4 vertices made with 3 60-degree angles coming together. 3x60=180 or deficit is 360-180=180 per vertex.
cube
'bathtub'
triangular-cylinder
trunctetrahedron
cubeoctahedron
icosahedron
snubcube