Locally toroidal regular polytopes of rank 4 |
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| Authors: | Peter McMullen Egon Schulte |
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| Affiliation: | (1) Department of Mathematics, University College London, WC1E 6BT London, England;(2) Department of Mathematics, Northeastern University, 02115 Boston, MA, USA |
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| Abstract: | The paper studies various relationships between locally toroidal regular 4-polytopes of types {6, 3,p} and {3, 6, 3}. These relationships are based on corresponding relationships between the regular honeycombs with the same Schläfli-symbol in hyperbolic 3-space. Also the paper discusses regular tessellations (secretions of rank 3) which are locally inscribed into regular 4-polytopes. In particular, this leads to local criteria for the finiteness of the polytopes. |
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