The CdCr2O4 spinel transforms to a 10.6% denser new polymorph of the CaFe2O4-type structure at 10 GPa and 1100 degrees C. This new polymorph has a honeycomb-like structure because of double rutile-type chains formed by [Cr-O-6] edge-shared octehedra. This crystal structure is prone to be magnetically frustrated and presents low-dimensional antiferromagnetism at 25 K < T < 150 K, accompanied by more complex interactions as the temperature decreases. These transitions are evidenced by magnetic susceptibility and heat capacity measurements. We also discuss a possible structural mechanism for the transformation.