MathDB

Let

T

be a regular tetrahedron. Let

t

be the regular tetrahedron whose vertices are the centers of the faces of

T

. Let

O

be the circumcenter of either tetrahedron. Given a point

P

different from

O

, let

m(P)

be the midpoint of the points of intersection of the ray

\overrightarrow{OP}

with

t

and

T

. Let

S

be the set of eight points

m(P)

where

P

is a vertex of either

t

T

. What is the volume of the convex hull of

S

divided by the volume of

t

Problem Statement