Ambiguous Object

Ambiguous Object
Heegyung Kim
October 12, 2021
George Mason University MATH 401: Mathematics Through 3D Printing

This object represents an ambiguous object, a mathematical optical illusion discovered by Kokichi Sugihara. He is a professor at Meiji University in Tokyo, Japan, and has won many awards in 3D optical illusions. When the object is reflected in a mirror, its appearance in the mirror is changed from the object that is being reflected. For my object, it forms a pentagon on one side and a circle on the other side when it is seen at a 45° angle downward. It is created by taking addition and difference between the functions for a pentagon and a circle.

From coding this object in Mathematica, there was a problem. I used the Piecewise function to build the diamond-shaped pentagon. However, it created a gap or space between the corners of the shape. This would make the object fall apart, not one piece object. So, I needed to create functions that would have the same interval and use the Show function to put all the pieces of the functions to make a pentagon. Overall, I used 6 functions to shape a pentagon and 2 functions to shape a circle.


For this assignment, I used Mathematica to build this object and exported it as an STL file. Ultimaker Cura was used to printing the object. It used the ABS Orange filament and a brim for the build plate adhesion. It took about 3 hours to print the object and the dimension was about 42 x 55.7 x 43.3 mm.


Source:
http://www.isc.meiji.ac.jp/~kokichis/Welcomee.html