Micrites capable of assembling into arbitrary shapes in three dimensions, with the constraint of a single species, might be most effectively fabricated in the shape of Platonic solids (regular polyhedra), to take advantage of maximum symmetry and to ensure that each polygon face of one micrite will perfectly coincide with the face of another micrite, thereby maximizing adhesion and minimizing stray fields. Only two of the regular polyhedra can be assembled to fill all space: the cube and the dodecahedron. Therefore, only the cube and dodecahedron are capable of constructing arbitrary shapes including the highest possible strength realized by a voidless solid. The dihedral angle between the adjoining faces of two cubes, joined by coinciding squares on a face of each cube, is 180°. Hence, it is difficult for an electric field, generated by charges on the perpendicular faces, to rotate the two cubes in such a way as to join at another pair of faces. The dodecahedron, however, has a corresponding dihedral angle of about 127° and a pair of dodecahedra can be easily caused to roll from one contact face to another. Therefore, the dodecahedron is the only space-filling Platonic solid that is also capable of easily-generated face-field-driven motion. I demonstrate that the micrites must be maintained in a fluid environment in order to provide sufficient lubrication for their polygonal binding surfaces to azimuthally rotate into coincidence. I calculate the speed of convergence in a lubricant environment and show that the distant micrites assemble only very slowly (for a practical range of parameters) unless there is some agitation of the fluid. I show how various solids can be constructed by convergence. I demonstrate how a primitive motor can be built from two dodecahedron-shaped micrites, and I calculate the maximum speed of the motor and the maximum power the motor can generate. I explain a surprisingly simple algorithm for a curious self-propelling flagellum constructed from a chain of dodecahedron-shaped micrites. I calculate the flagellum's maximum swimming speed and power consumption.
展开▼
