# Important announcement

We are constantly monitoring the situation concerning the spread of the coronavirus (COVID-19) and we decide to postpone the meeting. Based on the situation, we will make a final decision on the date of the event. The registration (via e-mail) will continue without changes. New deadlines for closing registration and for payments will be set in advance. The information will be available on the webpage and will be also sent to participants via e-mail. Stay in touch with us for new information.

Best wishes to all of you and your families,
The organizers of CS3 Workshop.

## Combinatorial structures on surfacesand their symmetries (CS3)

#### June 29 - July 3, 2020(postponed), Aveiro, Portugal

The workshop is dedicated to the honour of António Breda and Roman Nedela on the occasion of their 60th birthday.

Main topics of the workshop:
• Algebraic and topological graph theory
• Graph colourings
• Maps, hypermaps and related structures
• Abstract polytopes and related structures
• Riemann surfaces

#### Invited speakers

• Domenico Catalano (University of Aveiro, Portugal)
• Marston Conder (University of Auckland, New Zealand)
• Shaofei Du (Capital Normal University, Beijing, Public Republic of China)
• Gareth Jones (University of Southampton, United Kingdom)
• Alexander Mednykh (Sobolev Institute of Mathematics, Novosibirsk, Russia)
• Egon Schulte (Northeastern University, Boston, MA, United States)
• Jozef Širáň (Open University, Milton Keynes, United Kingdom and Slovak University of Technology, Bratislava, Slovakia)
• Martin Škoviera (Comenius University, Bratislava, Slovakia)
• Steve Wilson (Northern Arizona University, Flagstaff, AZ, United States)

#### Important dates

• Registration and abstract submission, by the end of January 2020,
• Early payment of fees, by the end of February 2020; (€250, €150 euros for students).
• Late payment of fees, from March by the end of May 2020 (€280, €170 euros for students).

#### Conference proceedings

All participants will be invited to submit a paper to a special issue of a journal (to be announced).

#### Organising committee

• Rui Duarte, (chair of organising committee)
• Ján Karabáš (website)
• Ilda Inácio, (local organiser)
• Kan Hu
If you want to contact the organisers directly, please send an email to Rui Duarte.

## Logo & Graphics

#### The Logo

The logo of the workshop is the dessin No. 440 in Census of Quadrangle Groups Inclusions. The census lists all inclusions of quadrangle groups (mainly in triangle groups). It was published in collateral note to the paper Quadrangle Groups Inclusions by António Breda, Roman Nedela, Domenico Catalano and Ján Karabáš.

The dessin d'enfant $$D$$ which represents the logo of CS3 corresponds to the coset action of subgroup $$S$$ of index $$60$$ in the triangle group $$\Delta(2,3,7)$$. The group $$S$$ is isomorphic to the quadrangle group $$Q(7,7,7,7)$$. The underlying surface of the embedding is an orbifold with signature $$(0;\{7,7,7,7\})$$ (not displayed here), the constellation which describes the map is $$(2^{30}, 3^{20}, 1^4.7^8)$$ and $$\operatorname{Mon}\, D \cong\mathrm{PSL}(2,29)$$ of order $$12180.$$

The diagram is created by Domenico Catalano.

#### Wall panelling in Alhambra

The group $$p6m$$ has one rotation centre of order six; it has two rotation centres of order three, which only differ by a rotation of $$60^\circ$$ (or, equivalently, $$180^\circ$$), and three of order two, which only differ by a rotation of $$60^\circ.$$ It has also reflections in six distinct directions. There are additional glide reflections in six distinct directions, whose axes are located halfway between adjacent parallel reflection axes. The corresponding Coxeter symbol is $$[6,3]$$ and Conway's orbifold signature is $$\ast 632.$$

The information is available on Wikipedia.

#### Persian Glased Tile

The group $$p4m$$ has two rotation centres of order four, and reflections in four distinct directions (horizontal, vertical, and diagonals). It has additional glide reflections whose axes are not reflection axes; rotations of order two are centred at the intersection of the glide reflection axes. All rotation centres lie on reflection axes. In the Coxeter notation is the group known as $$[4,4]$$ and Conway's orbifold signature is $$\ast 442.$$

The picture a and information available on Wikipedia .

#### Chinese Painting

The group $$p3m1$$ has three different rotation centres of order three. It has reflections in the three sides of an equilateral triangle. The centre of every rotation lies on a reflection axis. There are additional glide reflections in three distinct directions, whose axes are located halfway between adjacent parallel reflection axes. The corresponding Coxeter symbol is $$[3,3,3]$$ and Conway's orbifold signature is $$\ast 333.$$

The information is available on Wikipedia. The picture is available here.