DIRECTIONS:   In this applet, you can select several starting polyhedrons (Tetrahedron, Hexahedron, Octahedron, Cube, Dodecahedron, and a Polyehedral Torus) to set a starting polyhedral structure. This structural may be altered by moving the vertices (without affecting the existence of edges and faces) by dragging them in the image plane and using C and D to move in and out of the image plane in the parallel view in SELECT/MOVE mode. You can also add a vertex at the center of a face and triangulate the face creating more faces and edges, by pressing the SELECT/MOVE button to toggle to SELECT/INSERT mode. This shows the centroids of the visible faces in red. By clicking on centroid, you adds a vertex to the polyhedron at the centroid and triangulates the face the centroid lies on to create more faces and edges.

You have two original views of the surface a large view for manipulating and smaller view below the VIEW GENERATED and ITERATE buttons. Once the VIEW GENERATED button is pressed it becomes a VIEW ORIGINAL button, and you get to see one iteration of the surface by the Midpoint Method, the smaller view is not altered and shows the original surface used to generate the surface. The ITERATE button is now active and can be used to generate refinements of the surface by the Midpoint Method, the mini display always shows the original surface. Rotation of the surface by the arrow keys, rotates both the original mini display and the larger display of the generated surface.

Below the VIEW GENERATED/ORIGINAL and ITERATE buttons, the size of the displayed surface is given as a triple of numbers (F,E,V), where F = the number of faces, E = number of edges, and V = number of vertices. When viewing the iteration process, you can not alter any of the vertices or faces. But you can save the generated surface at any point, and reload that surface as a starting point, at which you can alter the surface as that becomes the original surface once it is loaded as an original surface.