HANDS ON LEARNING: GENERATING UNIT CELLS FOR VISUALLY IMPAIRED AND SIGHTED STUDENTS, ELEMENTARY THROUGH COLLLEGE LEVELS

Marbles, string, peg and Chinese checker boards, cardboard, round-headed straight pins and Tinker Toys are materials used to generate triangular and quadrilateral types which allow elementary to college level visually impaired or sighted students to gain an understanding of the geometric shapes that are used to generate unit cells. String inserted in holes outline translation distances and angles. Marbles mark nodes to generate square, rectangular, parallelogram and rhombohedra nets. Diamond lattices are formed from a centered rectangular net. Tracing quadrilaterals on non corrugated cardboard and cutting the quadrilaterals along their diagonals will form: right, right isosceles, isosceles, equilateral and scalene triangles. These triangles can only be reassembled into the quadrilaterals already generated. String connecting round-headed straight pins on corrugated cardboard provide students a variety of angles and translation lengths. Rectangular, square, parallelogram or isosceles nets can be made with Tinker toys. Unequal translation lengths perpendicular to these nets generates a primitive tetragonal, orthorhombic, monoclinic or hexagonal unit cell. If Tinker toy spools were spherical, an equal translation length at a right angle to a square net would form a primitive isometric unit cell. A body centered orthorhombic, tetragonal or isometric unit cell is formed by inserting at the center of one of these primitive unit cells an identical respective primitive lattice. Inserting a primitive isometric or orthorhombic unit cell in the center of the face of an identical primitive isometric or orthorhombic unit cell generates a face centered isometric or orthorhombic unit cell. The base centered monoclinic unit cell is formed by placing a lattice point in the center of the rectangular parts of the monoclinic primitive unit cell. Orthorhombic primitive unit cells contain three different size rectangles. Lattice points located in the center of one of the pair of rectangles of the primitive orthorhombic unit cell results in three possible orientations for an orthorhombic base centered unit cell. The rhombohedral unit cell is too difficult to construct. Students will increase their understanding of unit cells if they tactility examine models of the fourteen unit cells that are commercially available.