# Richard Klitzing

Dr. Richard Klitzing (born April 24th 1966) is a trained mathematician and trained physicist with a PhD in theoretical physics on the theory of quasicrystals that was granted by the Eberhard Karls University of Tübingen^{[1]}^{[2]}^{[3]}^{[4]}^{[5]}^{[6]}^{[7]}^{[8]}. After a short time of teaching in higher degree schools he abandoned the profession, later returning sporadically as an external part-time lecturer at the cooperative State University of Heidenheim.

As a spare-time mathematician, he is responsible for the discovery of several scaliform and CRF polytopes. For instance, the first ever known scaliforms tuta, and prissi have been discovered by him. He also discovered several of the scaliform diminishings of polytopes; eg. oddimo, kadify, and codify.

Besides inventing the concept of scaliforms he also invented the segmentotopes^{[9]} as a pedagogical means of easy to visualize monostratic polytopes, and researched on edge-facetings^{[10]}, e.g. he described first the chiral tetrahedral faceting quistet of sidtid. Further he expanded the concept of alternated faceting (aka snubbing) to alternations of higher-than-vertex elements^{[11]}, and he also expanded the notation of linearized Coxeter-Dynkin diagrams to include virtual nodes. He also contributed to the concept of tegum sums, initiated by Wout Gevaert.

He has his own website dedicated to polytopes [1], where he provides (currently) more than 9000 symmetry respecting incidence matrices for more than 4000 polytopes.

## References[edit | edit source]

- ↑ Klitzing, Richard (1996).
*Reskalierungssymmetrien quasiperiodischer Strukturen*(in German). Verlag Dr. Kovač. ISBN 978-3-86064-428-7. - ↑ Baake, M.; Klitzing, R.; Schlottmann, M. (1992). "Fractally Shaped Acceptance Domains of Quasiperiodic Square-Triangle Tilings with Dodecagonal Symmetry".
*Physica A*.**191**: 554–558. - ↑ Klitzing, R.; Schlottmann, M.; Baake, M. (1993). "Perfect Matching Rules for Undecorated Triangular Tilings with 10-, 12- and 8-fold Symmetry".
*Int. J. Mod. Phys. B*. 7, Nos. 6 & 7: 1455–1473. - ↑ Baake, M.; Ben-Abraham, S.I.; Klitzing, R.; Kramer, P.; Schlottmann, M. (1994). "Classification of Local Configurations in Quasicrystals".
*Acta Cryst., Sect. A50*.**5**: 553–566. - ↑ Klitzing, R.; Baake, M. (1994). "Representation of Certain Self-Similar Tilings with Perfect Matching Rules by Discrete Point Sets".
*J. Phys. I, France*.**4**: 893–904. - ↑ Klitzing, R. (1995). "Substitutional Tilings with Non-Degenerate Translational Modules, but with Vanishing Bragg Intensities".
*Proc. of the 5th Int. Conf. on Quasicrystals*. World Scietific, eds. C. Janot & R. Mosseri: 88–91. - ↑ Gähler, F.; Klitzing, R. (1997). "The Diffraction Pattern of Selfsimilar Tiling".
*The Mathematics of Long-Range Aperiodic Order, ed. R. V. Moody NATO Advanced Study Institute, Ser. C*. Kluwer.**489**: 141–174. - ↑ Papodopolos, Z.; Klitzing, R.; Kramer, P. (1997). "Quasiperiodic Icosahedral Tilings from the Six-Dimensional BBC Lattice".
*J. Phys: A: Math. Gen*. 30 No. 6: L143–L147. - ↑ Klitzing, R. (2000). "Convex Segmentochora".
*Symmetry: Culture and Science*. 11, Nos. 1-4: 139–181. - ↑ Klitzing, R. (2002). "Axial-Symmetrical Edge-Facetings of Uniform Polyhedra".
*Symmetry: Culture and Science*. 13, Nos. 3-4: 241–258. - ↑ Klitzing, R. (2010). "Snubs, Alternated Facetings, & Stott-Coxeter-Dynkin Diagrams".
*Symmetry: Culture and Science*. 21, No. 4: 329–344.