Toroid is a polyherdon homeomorphic to a torus with all faces simple polygons. The one shown below consists of 16 vertices, 32 edges and 16 faces. The Euler formula works as
V - E + F = 16 - 32 + 16 = 0 = 2 - 2·1
in agreement with the shape having one tunnel.
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Drag the mouse to rotate the prism. Use the right button to remove and put back individual faces.
(Acknowledgement: I have learned most of Java details from the implementation by Meiko Rachimow.)
Copyright © 1996-2018 Alexander Bogomolny