The results of a study of the mechanical properties of the honeycomb material made of polyamide-12, which consists of structural elements that repeat in three directions and have Schwartz primitive geometry, are presented. Samples in the form of a cube (size 30 × 30 × 30 mm) are obtained by layer-by-layer sintering of powder material on a 3D printer of selective laser sintering (SLS) type. Compression tests of samples with various geometry show that the strength of the samples increases with a decrease in the characteristic size of the repeating structural element. According to the calculations performed by the finite element method, this is caused by an increase in the dangerous sectional area. The possibility of a significant increase in the specific strength of the material while maintaining its density is shown.