### Table 1: Spherical Symmetry Groups Based on the Platonic Solids Symmetry Group Order Symmetry Operators

2001

"... In PAGE 2: ... Because the triangular faces no longer contain mirror symmetry con- straints, the tile boundaries can now be deformed to create intricate interlocking tile shapes. The straight and oriented tetrahedron are just two of the seven groups derived from the Platonic solids ( Table1 ). In addition to the straight and oriented octahedron/cube and icosahedron/dodecahedron, there is also the double tetrahe- dron group.... ..."

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### Table I. Elastic Characteristics of Rotational Symmetry Groups Rotational Independent symmetry

### Table 5. Numbers of HSs Belonging to Dillerent Symmetry Groups

"... In PAGE 6: ...Ie 21 26 The overall distributions into symmetry groups for HSs are 25 known completely for /r lt;16 according to another recent review. Table5 contains supplements to these data. For h gt; 17.... ..."

### Table 2. The size of the solution symmetry group and number of solutions for the n-queens problem with constraints to eliminate the constraint symmetry.

2005

"... In PAGE 19: ...resulting CSP by finding all the solutions and finding the automorphisms of the graph that has an n-ary hyperedge for every solution. Table2 shows the size of the solution symmetry group. Table 2.... ..."

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### Table 1: Cremmer-Julia symmetry groups and scalars, 1-forms and 2-forms.

"... In PAGE 3: ...3 Upon compacti cation on a torus Td, 11D SUGRA exhibits a group of continuous global symmetry G, as well as a (composite) gauge invariance under its R-symmetry maximal compact subgroup K, as listed in Table1 [8]. The symmetry can be seen among the scalar elds, which take value in the symmetric space KnG.... In PAGE 3: ... The symmetry group Gd acts on the right on the coset KnG, and induces a compensating moduli-dependent K-rotation to preserve the gauge K = 1. The massless spectrum also includes a number of p-forms, given for p = 1; 2 in the last two columns of Table1 , where dualization into forms of lower degree has been carried out. They transform linearly under G and induce charges for particles (m) and strings (n) respectively.... In PAGE 5: ... This is consistent with the fact that E9 is the a ne Lie group associated to E8, and implies that the representations are in nite dimensional. For d gt; 9, the symmetry is even more dramatic, with hyperbolic E10 or Kac-Moody E11, while for d lt; 9 we recover the groups in Table1 . The representations corresponding to the extremal nodes indicated in (13) correspond to a particle multiplet with highest weight M = 1=Rd (a KK mode) , a string multiplet with highest weight T1 = R1=l3 p (a singly wound M2-brane), and a membrane multiplet with highest weight 1=l3 p.... In PAGE 5: ... The representations corresponding to the extremal nodes indicated in (13) correspond to a particle multiplet with highest weight M = 1=Rd (a KK mode) , a string multiplet with highest weight T1 = R1=l3 p (a singly wound M2-brane), and a membrane multiplet with highest weight 1=l3 p. The particle and string multiplets are precisely the ones charged under the one- and two- form potentials in Table1 . The other members in the same multiplet are obtained by applying Weyl re ections on these highest weights, and e.... ..."

### Table 5 Overview of the dimension f of M and the dimension g of the global symmetry group G for various cameras.

2007

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### Table 2: Subgroups of symmetry group ? which are admissible for ows in the case that ? is a nite subgroup of O(2) (taken from [5]).

1996

"... In PAGE 6: ...5 Suppose ? is a nite subgroup of O(2), and ?. Then all sub- groups which are admissible for ows ft : IR2 7! IR2 with reversing symmetry group ? are listed in Table 1 and Table2 . The !-limit sets that realize admissibility can be taken to be Liapunov stable periodic orbits.... In PAGE 13: ... symmetric periodic orbit with Zn symmetry, cf. Fig. 1(c). The results are summarized in Table 1. Together with the results of [5] { which are summarized in Table2 { they cover all admissible nite subgroups of O(2) for ows in IR2. 6 Symmetric !-limit sets in xed point subspaces In this paper we have concentrated mainly on symmetric !-limit sets with trivial instantaneous symmetry, i.... ..."

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### Table 3 The dimension g of the global symmetry group G for the structure from motion problem in the case d = 2 for various cameras.

2007

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### Table 5.1: Gain in computational complexity depending on algorithm type for a few typical symmetry groups. Domain G jGj

2004

### Table 4 The dimension g of the global symmetry group G for the structure from motion problem in the case d = 3 for various cameras. The group of dilations is the group of symmetries generated by translations and scalings. The group of similarities is generated by translations, rotations and scalings. The Euclidean group is generated by rotations and translations.

2007

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