Journal of Mathematical Chemistry

, Volume 56, Issue 8, pp 2485–2494 | Cite as

\(PSL\left( 2,7\right) \) and carbon allotrope D168 Schwarzite

  • Qaiser Mushtaq
  • Nighat MumtazEmail author
Original Paper


We investigate actions of the modular group \(PSL(2, \mathbb {Z} )\) on the projective line over finite fields \(PL(\mathbf {F}_{7^{n}})\) and find interesting relation between the coset diagram of orbits and the carbon allotrope with negative curvature D168 Shewarzite. We also highlighted some topological aspects of these diagrams.


Projective special linear groups Heptakisoctahedral group Coset diagrams Genus Euler’s characteristics 

Mathematics Subject Classification

Primary 05C38 15A15 Secondary 05A15 15A18 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.The Islamia University of BahawalpurBahawalpurPakistan
  2. 2.Quaid-i-Azam UniversityIslamabadPakistan

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