A new geometric pattern

Five equally sized squares generate a complete set of 12 different figures (pieces, graphic A).
These pieces may be assembled in a grid of 8 × 8 squares, leaving the centre of 2 × 2 squares void (panel, graphic B). This is, by the way, only one of 65 solutions to solve this problem. The cluster of the three pieces “T”,”L” and “D” can be inverted, though. Six of these panels cover a die surface so that all pieces are oriented symmetrically to the centre of the die and simultaneously the total surface of the die is subdivided into three perfectly congruent pattern surfaces, each decomposed into the set of 12 pieces (patterns, graphic C and D). The void centre squares of the panels are “punched out”. The patterns are projected on the surface of a sphere (The Puzzled Sphere, graphic E).