Building Cylinders from Congruent Triangles
Connect the vertices of two polygons a unit distance apart to form a ring of equilateral triangles, also known as a skew prism; then build a tower of such rings. Spheres can be used to emphasize the vertices, or you can center them to create a structure similar to a buckytube. You can adjust the number of sides of the polygons: 2 produces a tetrahedron, 3 an octahedron, 4 a part of a gyroelongated square dipyramid, and 5 a part of an icosahedron. You can also vary the number of levels in the tower, the vertical extension of the triangles (1 gives the equilateral triangle, -1 gives zero height), and the size of the spheres.