Simplicial complexes
No. 113, 1973
(Algebraic topology)
India ink and pencil on paper, 30.5x43 cm.
On grainy, stepped pyramids rest massive stone monoliths, each a monument to the rigid, angular, and hard-edged life in this isolated world, devoid of faces. Human beings stand aligned before the stones, not even seeing the nearby flat hills, which are splotched and spare, without even a weed. The sky above is as bland as the world below. Only the stones define the desolate space. Underlying this scene is an idea, the notion of a simplicial complex, a polyhedron, the sum of building blocks glued together in a piecewise, linear structure. There are tetrahedra, prisms, polytopes, and cones over polygons, all different from each other and yet all composed of rectilinear tetrahedra. To make computations, topology employs homeomorphic images of balls, or cells, that come together to form cell complexes. In this picture, coarse, consolidated blocks dominate the scene—blocks that would suffice for computing many applied problems.
