Edge-transitive tessellations with non-negative Euler characteristic
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1 October, 2009 p. Edge-transitive tessellations with non-negative Euler characteristic Alen Orbanić Daniel Pellicer Tomaž Pisanski Thomas Tucker Arjana Žitnik
2 October, 2009 p. Maps 2-CELL EMBEDDING of a
3 October, 2009 p. Maps 2-CELL EMBEDDING of a 3-CONECTED GRAPH on a
4 October, 2009 p. Maps 2-CELL EMBEDDING of a 3-CONECTED GRAPH on a COMPACT CLOSED SURFACE
5 October, 2009 p. Maps 2-CELL EMBEDDING of a 3-CONECTED GRAPH on a COMPACT CLOSED SURFACE Automorphism automorphism of the graph that extends to an auto-homomeorphism of the surface.
6 October, 2009 p. Maps 2-CELL EMBEDDING of a 3-CONECTED GRAPH on a COMPACT CLOSED SURFACE Automorphism automorphism of the graph that extends to an auto-homomeorphism of the surface. Flag triple of incident vertex, edge and cell (face)
7 Flag graph October, 2009 p.
8 Flag graph October, 2009 p.
9 Flag graph October, 2009 p.
10 Flag graph October, 2009 p.
11 October, 2009 p. Delaney-Dress symbol Delaney-Dress symbol flag graph / automorphism group
12 October, 2009 p. Delaney-Dress symbol Delaney-Dress symbol flag graph / automorphism group
13 October, 2009 p. Delaney-Dress symbol Delaney-Dress symbol flag graph / automorphism group
14 October, 2009 p. Edge-transitive Edge-transitive maps have 1-2- or 4-orbits under the automorphism group
15 October, 2009 p. Edge-transitive Edge-transitive maps have 1-2- or 4-orbits under the automorphism group Edge type p,q;s,t
16 October, 2009 p. Edge-transitive Edge-transitive maps have 1-2- or 4-orbits under the automorphism group Edge type p,q;s,t p, q size of faces
17 October, 2009 p. Edge-transitive Edge-transitive maps have 1-2- or 4-orbits under the automorphism group Edge type p,q;s,t p, q size of faces s, t degrees of vertices
18 October, 2009 p. Edge-transitive Edge-transitive maps have 1-2- or 4-orbits under the automorphism group Edge type p,q;s,t p, q size of faces s, t degrees of vertices Edge homogeneous every edge has the same type
19 October, 2009 p. Edge-transitive Edge-transitive maps have 1-2- or 4-orbits under the automorphism group Edge type p,q;s,t p, q size of faces s, t degrees of vertices Edge homogeneous every edge has the same type On planar tessellations Edge-homogeneous edge-transitive
20 October, 2009 p. Spherical tessellations Tetrahedron 3,3;3,3
21 October, 2009 p. Spherical tessellations Tetrahedron 3,3;3,3 Cube 4,4;3,3
22 October, 2009 p. Spherical tessellations Tetrahedron 3,3;3,3 Cube 4,4;3,3 Octahedron 3,3;4,4
23 October, 2009 p. Spherical tessellations Tetrahedron 3,3;3,3 Cube 4,4;3,3 Octahedron 3,3;4,4 Dodecahedron 5, 5; 3, 3
24 October, 2009 p. Spherical tessellations Tetrahedron 3,3;3,3 Cube 4,4;3,3 Octahedron 3,3;4,4 Dodecahedron 5, 5; 3, 3 Icosahedron 3,3;5,5
25 October, 2009 p. Spherical tessellations Tetrahedron 3,3;3,3 Cube 4,4;3,3 Octahedron 3,3;4,4 Dodecahedron 5, 5; 3, 3 Icosahedron 3,3;5,5 Cuboctahedron 3, 4; 4, 4
26 October, 2009 p. Spherical tessellations Tetrahedron 3,3;3,3 Cube 4,4;3,3 Octahedron 3,3;4,4 Dodecahedron 5, 5; 3, 3 Icosahedron 3,3;5,5 Cuboctahedron 3, 4; 4, 4 Icosidodecahedron 3, 5; 4, 4
27 October, 2009 p. Spherical tessellations Tetrahedron 3,3;3,3 Cube 4,4;3,3 Octahedron 3,3;4,4 Dodecahedron 5, 5; 3, 3 Icosahedron 3,3;5,5 Cuboctahedron 3, 4; 4, 4 Icosidodecahedron 3, 5; 4, 4 Rhombic dodecahedron 4, 4; 3, 4
28 October, 2009 p. Spherical tessellations Tetrahedron 3,3;3,3 Cube 4,4;3,3 Octahedron 3,3;4,4 Dodecahedron 5, 5; 3, 3 Icosahedron 3,3;5,5 Cuboctahedron 3, 4; 4, 4 Icosidodecahedron 3, 5; 4, 4 Rhombic dodecahedron 4, 4; 3, 4 Rhombic triacontahedron 4, 4; 3, 5
29 Euclidean tessellations October, 2009 p.
30 Euclidean tessellations October, 2009 p.
31 Euclidean tessellations October, 2009 p.
32 Euclidean tessellations October, 2009 p.
33 Euclidean tessellations October, 2009 p.
34 October, 2009 p. Hyperbolic tessellations {3,7} {7,3}
35 October, 2009 p. Admissible types 1 p = q,s = t: regular (reflexible)
36 October, 2009 p. Admissible types 1 p = q,s = t: regular (reflexible) 2.1 s = t, even, p > q, both odd: vertex-transitive 2.2 s = t,p > q, all even: vertex-transitive 2.3 s = t, even, p > q, one odd: vertex-transitive
37 October, 2009 p. Admissible types 1 p = q,s = t: regular (reflexible) 2.1 s = t, even, p > q, both odd: vertex-transitive 2.2 s = t,p > q, all even: vertex-transitive 2.3 s = t, even, p > q, one odd: vertex-transitive 3.1 s > t,p = q, all even: face-transitive 3.2 p = q, even, s > t, one odd: face-transitive 3.3 p = q, even, s > t, both odd: face-transitive
38 October, 2009 p. Admissible types 1 p = q,s = t: regular (reflexible) 2.1 s = t, even, p > q, both odd: vertex-transitive 2.2 s = t,p > q, all even: vertex-transitive 2.3 s = t, even, p > q, one odd: vertex-transitive 3.1 s > t,p = q, all even: face-transitive 3.2 p = q, even, s > t, one odd: face-transitive 3.3 p = q, even, s > t, both odd: face-transitive 4 p > q,s > t, all even
39 October, 2009 p. 1 Compact surfaces Edge-transitive maps on compact surfaces
40 October, 2009 p. 1 Compact surfaces Edge-transitive maps on compact surfaces quotients of an edge-transitive planar tessellation
41 October, 2009 p. 1 Compact surfaces Edge-transitive maps on compact surfaces quotients of an edge-transitive planar tessellation Quotients of the sphere
42 October, 2009 p. 1 Compact surfaces Edge-transitive maps on compact surfaces quotients of an edge-transitive planar tessellation Quotients of the sphere Projective plane
43 October, 2009 p. 1 Compact surfaces Edge-transitive maps on compact surfaces quotients of an edge-transitive planar tessellation Quotients of the sphere Projective plane Quotients of the Euclidean plane
44 October, 2009 p. 1 Compact surfaces Edge-transitive maps on compact surfaces quotients of an edge-transitive planar tessellation Quotients of the sphere Projective plane Quotients of the Euclidean plane Torus, Klein bottle
45 Projective plane October, 2009 p. 1
46 October, 2009 p. 1 Projective plane Hemi-cube 4,4;3,3
47 October, 2009 p. 1 Projective plane Hemi-cube 4,4;3,3 Hemi-octahedron 3, 3; 4, 4
48 October, 2009 p. 1 Projective plane Hemi-cube 4,4;3,3 Hemi-octahedron 3, 3; 4, 4 Hemi-dodecahedron 5, 5; 3, 3
49 October, 2009 p. 1 Projective plane Hemi-cube 4,4;3,3 Hemi-octahedron 3, 3; 4, 4 Hemi-dodecahedron 5, 5; 3, 3 Hemi-icosahedron 3, 3; 5, 5
50 October, 2009 p. 1 Projective plane Hemi-cube 4,4;3,3 Hemi-octahedron 3, 3; 4, 4 Hemi-dodecahedron 5, 5; 3, 3 Hemi-icosahedron 3, 3; 5, 5 Hemi-cuboctahedron 3, 4; 4, 4
51 October, 2009 p. 1 Projective plane Hemi-cube 4,4;3,3 Hemi-octahedron 3, 3; 4, 4 Hemi-dodecahedron 5, 5; 3, 3 Hemi-icosahedron 3, 3; 5, 5 Hemi-cuboctahedron 3, 4; 4, 4 Hemi-icosidodecahedron 3, 5; 4, 4
52 October, 2009 p. 1 Projective plane Hemi-cube 4,4;3,3 Hemi-octahedron 3, 3; 4, 4 Hemi-dodecahedron 5, 5; 3, 3 Hemi-icosahedron 3, 3; 5, 5 Hemi-cuboctahedron 3, 4; 4, 4 Hemi-icosidodecahedron 3, 5; 4, 4 Hemi-rhombic dodecahedron 4, 4; 3, 4
53 October, 2009 p. 1 Projective plane Hemi-cube 4,4;3,3 Hemi-octahedron 3, 3; 4, 4 Hemi-dodecahedron 5, 5; 3, 3 Hemi-icosahedron 3, 3; 5, 5 Hemi-cuboctahedron 3, 4; 4, 4 Hemi-icosidodecahedron 3, 5; 4, 4 Hemi-rhombic dodecahedron 4, 4; 3, 4 Hemi-rhombic triacontahedron 4, 4; 3, 5
54 Torus October, 2009 p. 1
55 Torus October, 2009 p. 1
56 Torus October, 2009 p. 1
57 Klein bottle October, 2009 p. 1
58 October, 2009 p. 1 Admissible types 1 p = q,s = t: regular (reflexible) 2.1 s = t, even, p > q, both odd: vertex-transitive 2.2 s = t,p > q, all even: vertex-transitive 2.3 s = t, even, p > q, one odd: vertex-transitive 3.1 s > t,p = q, all even: face-transitive 3.2 p = q, even, s > t, one odd: face-transitive 3.3 p = q, even, s > t, both odd: face-transitive 4 p > q,s > t, all even
59 October, 2009 p. 1 Admissible types Every edge-transitive tessellation has one of the previous admissible types
60 October, 2009 p. 1 Admissible types Every edge-transitive tessellation has one of the previous admissible types There are infinitely many maps on compact closed surfaces with any given hyperbolic type
61 Flag graphs October, 2009 p. 1
62 Flag graphs October, 2009 p. 1
63 October, 2009 p. 2 Higher genus Alen s Orbanić s PhD
64 October, 2009 p. 2 Higher genus Alen s Orbanić s PhD Edge type
65 October, 2009 p. 2 Higher genus Alen s Orbanić s PhD Edge type Delaney-Dress graph
66 October, 2009 p. 2
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