Reaching high densities is a key step toward cold-collision experiments with polyatomic molecules. We use a cryofuge to load up to
2
×
10
7

CH
3
F
molecules into a boxlike electric trap, achieving densities up to
10
7
/
cm
3
at temperatures around 350 mK where the elastic dipolar cross section exceeds
7
×
10
−
12
 
 
cm
2
. We measure inelastic rate constants below
4
×
10
−
8
 
 
cm
3
/
s
and control these by tuning a homogeneous electric field that covers a large fraction of the trap volume. Comparison to ab initio calculations gives excellent agreement with dipolar relaxation. Our techniques and findings are generic and immediately relevant for other cold-molecule collision experiments.