Kissing the Archimedeans

<p>In this paper the three dimensional kissing problem will be related to the Platonic and Archimedean solids. On each polyhedra presented their vertices will have spheres expanding such that the center of each of these outer spheres are the vertices of the polyhedron, and these outer spheres will continue to expand until they become tangent to each other. The ratio will be found between the radius of each outer sphere, and the radius of an inner sphere such that each inner sphere's center is the circumcenter of the polyhedron, and the inner sphere is tangent to each outer sphere. Every Platonic and Archimedean solid has a unique outer sphere to inner sphere ratio. The circumradius of the Platonic and Archimedean solids will be found by solving for the circumradius of the polyhedra's vertex figure. After the circumradius is found, the relation between the edge length of the solids, and the circumradius is converted to the radius of the outer spheres, r, and the radius of the inner sphere, R.</p>

Name thesis:degree_name

Master of Science

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Math and Computer Science

Year dc:date.available

2022

Author dc:creator

• Webb, Anthony

Contributors dc:contributor

• Daniel Rowe

• Platonic
• Archimedean
• Circumcenter
• Circumradius
• Polyhedra
• Kissing
• Algebra
• Algebraic Geometry
• Geometry and Topology

Repository record dc:identifier

https://commons.nmu.edu/theses/713

OAI identifier oai:identifier

oai:commons.nmu.edu:theses-1751