MathDB

Given a triangle, its midpoint triangle is obtained by joining the midpoints of its sides. A sequence of polyhedra

P_{i}

is defined recursively as follows:

P_{0}

is a regular tetrahedron whose volume is 1. To obtain

P_{i+1}

, replace the midpoint triangle of every face of

P_{i}

by an outward-pointing regular tetrahedron that has the midpoint triangle as a face. The volume of

P_{3}

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. Find

m+n

Problem Statement