Following a head impact, EPS foam bicycle helmets effectively mitigate translational kinematics (linked to skull fracture) but not rotational kinematics (associated with traumatic brain injury (TBI)). Honeycomb structures can potentially be an advantageous alternative to foam due to their superior energy absorption potential and anisotropic properties. Specifically, honeycomb allows deformation in the shear loading direction to absorb impact energy that causes rotational head kinematics. In beeswax, pentagons and heptagons (called ‘5-7 defects’) are observed within the array of hexagons in areas of curvature. In this study, a new helmet design was proposed that uses hexagonal honeycomb with 5-7 defects to accommodate the curvature of the human head. Out-ofplane compressive properties of the design (relevant to skull fracture protection) were explored. The optimal design would maximize energy absorption per unit volume (Uv) while maintaining peak stress (σp) just below the injury threshold for skull fracture. Various honeycomb designs, including regular honeycomb (with six variations in relative density (̅ρ)), and honeycomb with 5-7 defects were 3D-printed with thermoplastic polyurethane. Quasi-static (strain rate of 10-3 /s) out-of-plane compression tests were performed. There were no notable differences in mechanical properties between samples with and without 5-7 defects, indicating that 5-7 defects do not reduce the energy absorbing capability. Increasing ̅ρ from 14 to 28% resulted in a linear increase in both σp and Uv. Using an injury threshold for skull fracture of 2.25 MPa, the maximum allowable honeycomb ̅ρ was determined to be 36%. Compression tests were also performed at strain rates of 0.03 /s and 0.06 /s and the results indicated there was no strain rate dependence over this range. The present work demonstrates the design is capable of protecting against skull fracture. This is the first stage towards determining the optimal honeycomb design for head protection, where future work will focus on reducing the risk of TBI.