Hereditary Polytopes

Every regular polytope has the remarkable property that it inherits all symmetries of each of its facets. This property distinguishes a natural class of polytopes which are called hereditary. Regular polytopes are by definition hereditary, but the other polytopes in this class are interesting, have possible applications in modeling of structures, and have not been previously investigated. This paper establishes the basic theory of hereditary polytopes, focussing on the analysis and construction of hereditary polytopes with highly symmetric faces.Comment: Discrete Geometry and Applications (eds. R.Connelly and A.Ivic Weiss), Fields Institute Communications, (23 pp, to appear

Faculty wisdom as teaching culture care within the indigenous context of the Southeastern United States

This poster presents an ethnonursing research study guided by the culture care theory entitled Nursing Faculty Care, Expressions, Patterns, and Practices Related to Teaching Culture Care and conducted within the environmental context of urban and rural baccalaureate nursing programs in the Southeastern United States. The goal of the study was to discover faculty care that facilitated teaching students to provide culturally congruent and competent care. Four universal themes with universal and diverse patterns which supported the themes were discovered. The themes were faculty care as embedded in Christian religious values, beliefs, and practices; faculty teaching culture care without an organizing conceptual framework; faculty providing generic and professional care to nursing students; and care as essential for faculty health and well being to teach culture care. Discoveries for nursing actions and decisions for teaching culture care and two newly discovered care constructs, care as mentoring and Christian care are presented. This study, a unique application of the culture care theory, contributed to understanding the complex nature of teaching culture care and to the body of transcultural nursing education knowledge and the discipline of nursing

And then they boned: an analysis of fanfiction and its influence on sexual development

The purpose of this research is to demonstrate how young adults come to understand their sexuality (from sexual and gender identities to sexual likes and dislikes) through reading and writing fanfiction. Previous studies show that fanfiction promotes non-heterosexual orientations, but little research has been done on how it contributes to overall sexual development. In conducting an online survey of fanfiction readers, I explore how fans use these works to generate an understanding of themselves as sexual beings. Explicit stories make up a sizable portion of the fanfiction available, and there is a wide range of sexual acts depicted in those stories; ones that readers may not have been introduced to otherwise. Fanfiction can also facilitate discussion of sexuality and gender identity, topics that may not be appropriate in other social spheres, which can assist further sexual development. This study looks at just how influential fanfiction, and the fanfiction community, can be on sexual development

Internal and external duality in abstract polytopes

We define an abstract regular polytope to be internally self-dual if its self-duality can be realized as one of its symmetries. This property has many interesting implications on the structure of the polytope, which we present here. Then, we construct many examples of internally self-dual polytopes. In particular, we show that there are internally self-dual regular polyhedra of each type $\{p, p\}$ for $p \geq 3$ and that there are both infinitely many internally self-dual and infinitely many externally self-dual polyhedra of type $\{p, p\}$ for $p$ even. We also show that there are internally self-dual polytopes in each rank, including a new family of polytopes that we construct here

Algorithms for classifying regular polytopes with a fixed automorphism group

In this paper, various algorithms used in the classifications of regular polytopes for given groups are compared. First computational times and memory usages are analyzed for the original algorithm used in one of these classifications. Second, a possible algorithm for isomorphism testing among polytopes is suggested. Then, two improved algorithms are compared, and finally, results are given for a new classification of all regular polytopes for certain alternating groups and for the sporadic group $Co_3$