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String C-groups from groups of order 2^m and exponent at least 2^(m - 3)
This work provides a classification of string C-groups of order 2m and exponent at least 2^(m - 3). Prior to the classification, we complete the list of groups of exponent 2^(m - 3) and rank at leastExpand
Symmetry groups of single-wall nanotubes.
This work investigates the symmetry properties of single-wall carbon nanotube and their structural analogs, which are nanotubes consisting of different kinds of atoms, by looking at symmetries and color fixing symmetry associated with a coloring of the tiling by hexagons in the Euclidean plane. Expand
Colorings of single-wall carbon nanotubes
Abstract In this work, we describe a process to classify and characterize nanotubes with several types of atoms by constructing colorings associated with single-wall carbon nanotubes. We alsoExpand
String C-groups of order 1024
This paper determines the non-degenerate string C-groups of order 1024 by using the technique of central extension ofstring C- groups of order 512 to compute for quotients of universal string C -groups. Expand
Symmetry groups associated with tilings on a flat torus.
This work investigates symmetry and color symmetry properties of Kepler, Heesch and Laves tilings embedded on a flat torus and their geometric realizations as tilings on a round torus in EuclideanExpand
A quotient space approach to model nanotori and determine their symmetry groups
This paper discusses a geometric model of a nanotorus based on the concept of quotient spaces. The derivation of the symmetry group of the embedded toroidal quotient space in the 4-dimensional flatExpand
Designing Mobile Apps to Promote Numeracy and Statistical Reasoning
Even with major advancements in the field of mathematics education, many students still do not attain the learning competencies prescribed by official curricula. This may be partially explained byExpand
Geometric realizations of regular abstract polyhedra with automorphism group $H_3$
A \textit{geometric realization} of an abstract polyhedron $\mathcal{P}$ is a mapping $\rho : \mathcal{P} \to \mathbb{E}^3$ that sends an $i$-face to an open set of dimension $i$. This work adapts aExpand
Revisiting a Number-Theoretic Puzzle: The Census-Taker Problem
The current work revisits the results of L.F. Meyers and R. See in [3], and presents the census-taker problem as a motivation to introduce the beautiful theory of numbers.