We classify integral rootless lattices which are sums of pairs of EE8-lattices (lattices isometric to √ 2 times the E8-lattice) and which define dihedral groups of orders less than or equal to 12. Most of these may be seen in the Leech lattice. Our classification may help understand Miyamoto involutions on lattice type vertex operator algebras and give a context for the dihedral groups which oc...

The Fourier transforms x̂j = ∑ k xkω , k, j = 0, 1, . . . , n− 1 of a data vector x with scalar components xk indexed by n-fold planar rotations ω k define a n × n Hermitian matrix F with entries ωjk/√n, so that x̂ = √n Fx and the inverse Fourier transform is simply x = F∗x̂/√n. Here, the frequencies ω and their harmonics ω fully describe the set (Ĝ) of all n irreducible representations of the Abe...

Dihedral Golay sequences are introduced and found for lengths 7,9,15, and 19. Applications include new classes of signed group Hadamard matrices and 19 real Hadamard matrices of orders 2p, p S 4169.

The Pt(II) ion in the title complex, [PtBr(2)(C(14)H(10)N(4))], has a slightly distorted square-planar environment defined by the two pyridyl N atoms of the chelating 2,3-di-2-pyridyl-pyrazine ligand and two bromide anions. In the crystal, the pyridyl rings are considerably inclined to the least-squares plane of the PtBr(2)N(2) unit [maximum deviation = 0.064 (2) Å] with dihedral angles of 65.2...

‎In this work‎, ‎a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$‎. ‎Each element of the sequence represents a vertex of the polygon‎. ‎Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis‎. ‎Here each symmetry is considered as a system that takes an input circular sequence and g...

A non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized Fibonacci sequence , , , . A remarkable application of this definition may be find on the study of random covers in the cryptography. The 2-step generalized sequences for the dihedral groups studi...

We construct rank 2 thick nondiscrete affine buildings associated with an arbitrary finite dihedral group.