This paper proposes a generally new type of macrospace filling honeycombs having quasi-regular pentahedral cells with skew hexagonal faces. Two discoveries allow fundamentally diverse macrostructural systems to be offered for the synthesis of minimum mass and maximum stiffness constructions, as well as analysis of large scale structures of Universe. An existence of spatial cells named pentahedra is demonstrated by topological transformations of hexagonal prismatic honeycomb and is based on a recently discovered Phi relationship within a regular hexagonal tessellation. We study geometrical symmetry of this honeycomb, filling space with no gaps or overlaps. Finally it is pointed out that abstract or skeletal analogues of pentahedral honeycomb have effective practical uses by synthesis of artificial man-made macromedium, especially in orbital large scale structural systems.