The Orbifold Notation for Two-Dimensional Groups

  title={The Orbifold Notation for Two-Dimensional Groups},
  author={John H. Conway and Daniel H. Huson},
  journal={Structural Chemistry},
This paper gives a detailed introduction to the orbifold notation for two-dimensional (2-D) symmetry groups. It discusses the correspondence between properties of orbifolds and symmetries in the original surface. The problem of determining a group in situ is addressed. Elementary proofs of the classification of the Euclidean and spherical 2-D symmetry groups are presented. 

A topological proof of the modified Euler characteristic based on the orbifold concept

The vanishing of the modified Euler characteristic for symmetrically arranged space-filling polytopes is given a general proof based on the topological concept of orbifolds. The modified Euler

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A note on the two symmetry-preserving covering maps of the gyroid minimal surface

Abstract.Our study of the gyroid minimal surface has revealed that there are two distinct covering maps from the hyperbolic plane onto the surface that respect its intrinsic symmetries. We show that

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We present a technique for the enumeration of all isotopically distinct ways of tiling, with disks, a hyperbolic surface of finite genus, possibly nonorientable and with punctures and boundary. This



Generators and relations for discrete groups

1. Cyclic, Dicyclic and Metacyclic Groups.- 2. Systematic Enumeration of Cosets.- 3. Graphs, Maps and Cayley Diagrams.- 4. Abstract Crystallography.- 5. Hyperbolic Tessellations and Fundamental

The geometry and topology of three-manifolds

Visions of Symmetry: Notebooks, Periodic Drawings and Related Work of M. C. Escher by Doris Schattschneider (review)

Visions of symmetry contains Esch r's complete set of symmetry drawings reproduced in full colour and two Escher notebooks (which contain his theory of symmetry). In all, there are more than 350


  • J . Math .
  • 1967