Certain surfaces created by the enclosures of various torus curves are popular mathematical icons, most notably including the Mo ̈bius strip and art of twisted tori. Minimal surfaces are also popular due to typically smooth curvature and can be combined with torus curves; a minimal surface formed on a (2,1) torus knot is a smooth Mo ̈bius strip. By considering the minimal surfaces of (3,1) and higher torus curves, versions of twisted tori are created that enclose volumes with cross sections of concave polygons. Torus knot minimal surfaces are interesting as they contain one outer surface; the (4,1) torus knot is reminiscent of a Penrose triangle with rounded corners. Since the multiply symmetric volume is enclosed by a smooth outer surface, the shape has a modern aesthetic potentially useful in jewelry and architecture and may also have applications in material science and engineering as a minimal surface.