2024 Geo Problem 7
Source:
April 15, 2024
geometry
Problem Statement
An irregular octahedron has eight faces that are equilateral triangles of side length . However, instead of each vertex having four "neighbors" (vertices that share an edge with it) like in a regular octahedron, for this octahedron, two of the vertices have exactly three neighbors, two of the vertices have exactly four neighbors, and two of the vertices have exactly five neighbors. Compute the volume of this octahedron.Proposed by Connor Gordon