Coloring Uniform Honeycombs

In this paper, we discuss a method of arriving at colored three-dimensional uniform honeycombs. In particular, we present the construction of perfect and semi-perfect colorings of the truncated and bitruncated cubic honeycombs. If G is the symmetry group of an uncolored honeycomb, a coloring of the honeycomb is perfect if the group H consisting of elements that permute the colors of the given coloring is G. If H is such that [G:H] = 2, we say that the coloring of the honeycomb is semi-perfect

On subgroups of hyperbolic tetrahedral Coxeter groups

In this work we address the problem on the determination of the subgroup structure of crystallographic groups in hyperbolic space by deriving the low index subgroups of hyperbolic tetrahedral Coxeter groups and tetrahedral Kleinian groups. This paper continues the work giv en in [5, 6] on the subgroups of triangle groups

Coxeter Groups in Colored Tilings and Patterns

This paper illustrates a number of ways that color symmetry theory can be used as a tool to study abstract groups such as Coxeter groups

Hyperbolic Semi-regular Tilings and their Symmetry Properties

In this paper, symmetry groups of certain classes of semi-regular tilings on the hyperbolic plane are discussed

Understanding and Modeling of Grain Boundary Pinning in Inconel 718

The microstructure stability during δ sub-solvus annealing was investigated in Inconel 718 alloy. A reference dynamically recrystallized microstructure was produced through thermomechanical processing (torsion). The reference microstructure evolution during annealing was analyzed by EBSD (grain size, intragranular misorientation) and SEM (Σ <5 phase particles). Results confirm that, in the absence of stored energy, the grain structure is controlled by the δ phase particles, as predicted by the Zener equation. If the reference microstructure is strained (å < 0.1) before annealing, then stored energy gradients between grains will induce selective grain growth leading to coarsening. The phenomenon is controlled by the balance of three forces (acting on boundaries migration) having the same order of magnitude: capillarity, stored-energy and pinning forces. All these forces could be modeled in a single framework by the level set method. The first numerical results demonstrate the capability of the method to simulate 2D Zener pinning. © 2012 The Minerals, Metals, & Materials Society. All rights reserved

An Approach in Coloring Semi-regular Tilings on the Hyperbolic Plane

A coloring of a semi-regular tiling is perfect if every symmetry of the tiling permutes the colors of the tiling. In this paper, an approach to the construction of perfect colorings of semi-regular tilings on the hyperbolic plane is presented