MathDB

homothetic polyhedrons

Source: VI Soros Olympiad 1999-00 Round 1 11.6 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 21, 2024

geometry3D geometryhomothety

Problem Statement

It is known that a

n

-vertex contains within itself a polyhedron

M

with a center of symmetry at some point

Q

and is itself contained in a polyhedron homothetic to

M

with a homothety center at a point

Q

and coefficient

k

. Find the smallest value of

k

if a)

n = 4

, b)

n = 5