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Isogonal figure

In geometry, a polytope is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure. This implies that each vertex is surrounded by the same kinds of face in the same or reverse order, with the same angles between corresponding faces. Technically, we say that for any two vertices there exists a symmetry of the polytope mapping the first isometrically onto the second. Other ways of saying this are that the group of automorphisms of the polytope is transitive on its vertices, or that the vertices lie within a single symmetry orbit. All vertices of a finite n-dimensional isogonal figure exist on an -sphere; the term isogonal has long been used for polyhedra. Vertex-transitive is a synonym borrowed from modern ideas such as graph theory; the pseudorhombicuboctahedron –, not isogonal – demonstrates that asserting that "all vertices look the same" is not as restrictive as the definition used here, which involves the group of isometries preserving the polyhedron or tiling.

All regular polygons and regular star polygons are isogonal. The dual of an isogonal polygon is an isotoxal polygon; some even-sided polygons and apeirogons which alternate two edge lengths, for example a rectangle, are isogonal. All planar isogonal 2n-gons have dihedral symmetry with reflection lines across the mid-edge points. An isogonal polyhedron and 2D tiling has a single kind of vertex. An isogonal polyhedron with all regular faces is a uniform polyhedron and can be represented by a vertex configuration notation sequencing the faces around each vertex. Geometrically distorted variations of uniform polyhedra and tilings can be given the vertex configuration. Isogonal polyhedra and 2D tilings may be further classified: Regular if it is isohedral and isotoxal. Quasi-regular if it is isotoxal but not isohedral. Semi-regular if every face is a regular polygon but it is not isotoxal. Uniform if every face is a regular polygon, i.e. it is quasiregular or semi-regular. Semi-uniform if its elements are isogonal.

Scaliform if all the edges are the same length. Noble if it is isohedral; these definitions can be extended to higher-dimensional tessellations. All uniform polytopes are isogonal, for example, the uniform 4-polytopes and convex uniform honeycombs; the dual of an isogonal polytope is an isohedral figure, transitive on its facets. A polytope or tiling may be called k-isogonal. A more restrictive term, k-uniform is defined as an k-isogonal figure constructed only from regular polygons, they can be represented visually with colors by different uniform colorings. Edge-transitive Face-transitive Peter R. Cromwell, Cambridge University Press 1997, ISBN 0-521-55432-2, p. 369 Transitivity Grünbaum, Branko. C.. Tilings and Patterns. W. H. Freeman and Company. ISBN 0-7167-1193-1. Weisstein, Eric W. "Vertex-transitive graph". MathWorld. Olshevsky, George. "Transitivity". Glossary for Hyperspace. Archived from the original on 4 February 2007. Olshevsky, George. "Isogonal". Glossary for Hyperspace. Archived from the original on 4 February 2007.

Isogonal Kaleidoscopical Polyhedra Vladimir L. Bulatov, Physics Department, Oregon State University, Presented at Mosaic2000, Millennial Open Symposium on the Arts and Interdisciplinary Computing, 21–24 August 2000, Seattle, WA VRML models Steven Dutch uses the term k-uniform for enumerating k-isogonal tilings List of n-uniform tilings Weisstein, Eric W. "Demiregular tessellations". MathWorld


Fozzy is an American heavy metal band formed in Atlanta, Georgia, in 1999 by lead singer Chris Jericho and guitarist Rich Ward. The band has released three studio albums through this label; the band's current lineup consists of Jericho, Frank Fontsere, Billy Grey and Randy Drake. Jericho has characterized the band by saying, "If Metallica and Journey had a bastard child, it would be Fozzy." As of October 2017, the band has released one live album. Their first two albums consist of cover songs with some original material, while their albums since have made original material the primary focus. Fozzy started as Fozzy Osbourne, a play on the name of the singer Ozzy Osbourne, was a cover band assembled by Ward from whatever musicians he could find in a given week. In 1999, Jericho and Ward met in San Antonio, Texas after a wrestling show and Jericho was invited to play with the band, their first show was held in the downtown square of Marietta. Jericho did not plan to play with them permanently. In 2000, Jericho rejoined the band and became its front man under the persona of Moongoose McQueen, the band went on tour.

As part of the band's "gimmick", Jericho refused to acknowledge that Moongoose McQueen and Chris Jericho were the same person. When interviewed as Moongoose, he would stay in character the whole time and feign ignorance of who Chris Jericho was. On the other side, Chris Jericho was a "huge fan" of Fozzy; the band shortened its name to Fozzy, adopted the satirical back-story that they had signed with a record company to move to Japan to be huge rock stars, but the company went out of business, leaving them stranded for 20 years, while all their demos were snatched and recorded by other bands. Soon afterward, Fozzy produced their first album, self-titled and featuring covers of bands such as Dio, Twisted Sister, Iron Maiden, Mötley Crüe and Judas Priest. At one time the band considered changing their name to Big City Knights. Fozzy's second album, was produced in 2002, again with covers of bands such as Black Sabbath, Scorpions, W. A. S. P. and Accept. After the Happenstance tour ended in 2003, the band dropped its back-story and Chris Jericho's McQueen persona.

In January 2005, they released their third album, All That Remains, which had original tracks, including the singles "Enemy", "It's A Lie", "Born Of Anger", "The Test". All That Remains included guest appearances by musicians Zakk Wylde, Bone Crusher, Mark Tremonti, Myles Kennedy, Marty Friedman and Butch Walker; the album sold over 100,000 copies. In 2005, "Enemy" was the theme song for WWE No Way Out and in 2006 for a promotional video for TNA Bound for Glory. In 2005, the band played the Download Festival at England. Soon after the release of All That Remains, a fourth album was announced. On March 4, 2009, reported that Fozzy had signed a worldwide record deal with Australian-based Riot! Entertainment to release their fourth album; the album's lead single, "Martyr No More", was announced as an official theme song for the WWE Royal Rumble pay per view. The album was released in America followed by Australia and Europe. On February 19, 2011, Jericho said during an interview with Active Rock radio station WBSX in Wilkes-Barre, that he had completed lyrics for a brand new Fozzy album and that Ward was beginning work on writing the music.

The band hoped to have the new album released in February 2012. According to Fozzy's official Facebook page, the recordings were done on May 4, 2012. Fozzy released a brand new music video on June 7, shot at the Golden Gods Awards for the track "God Pounds His Nails". On July 10, Fozzy played the Sonisphere Festival at England. A special, two-CD edition of Fozzy's live album Remains Alive was released with Chasing the Grail on July 18; the band announced a headlining tour of the United Kingdom for November 2011. On September 9, Sean Delson announced his "retirement" from Fozzy as their bass guitar player to resume work with Agent Cooper. Fozzy announced the bass guitarist for Adrenaline Mob, as his replacement. On January 18, 2010, it was announced that Fozzy had signed with Century Media Records, planned to release a new album in the year. Jericho hinted the new album on his Twitter page, saying,'New @FOZZYROCK album in August?!'. Jericho made a full-time return to the WWE on January 4, but despite this, Fozzy was announced to be a part of the Download Festival in the UK, in the summer.

On July 17, Fozzy released the first single from their fifth studio album and Bones, titled "Sandpaper". The song features guest vocals by M. Shadows from Avenged Sevenfold and was the Hell in a Cell theme song. Sin and Bones was released on August 14. Shortly after the album's release, Chris Jericho once again left the WWE with his final appearance being on SmackDown, on August 20, so that he could go on tour with the band. Fozzy played on the 2012 Uproar Festival tour. After the Uproar Festival, Fozzy scheduled an international tour with stops in Australia. Fozzy made their return to the U. S. in 2013 touring as an opener for Saxon on the "Sacrifice and Sin" tour. One tour date was rescheduled and became a Fozzy solo date on October 16. During 2013, it was confirmed that Fozzy would begin working on a new record in 2014 and would be looking for a release date during the summer of 2014; the band entered the st

Pagan Kennedy

Pagan Kennedy is an American columnist and author, pioneer of the 1990s zine movement. She has written ten books in a variety of genres, was " regular contributor to the Boston Globe, has published articles in dozens of magazines and newspapers." In 2012–13, she was a New York Times Magazine columnist. Born Pamela Kennedy around 1963, she grew up in suburban Washington, D. C, she graduated from Wesleyan University in 1984, spent a year in the Masters of Fine Arts program at Johns Hopkins University. Kennedy's autobiographical zine Pagan's Head detailed her life during her twenties. Kennedy wrote a biography called The First Man-Made Man about Michael Dillon who in the 1940s was the first successful case of female-to-male sex change treatment, it describes how he fell in love with a male-to-female transsexual, Roberta Cowell, at the time the only other transsexual in Britain. In July 2012, Kennedy was named design columnist for the New York Times Magazine, her column, "Who Made That," detailed the origins of everything from the cubicle to the home pregnancy test.

Kennedy resigned from the column after signing a contract with Houghton Mifflin Harcourt to write a book, Inventology. Kennedy was a visiting professor of creative writing at Dartmouth College, taught fiction and nonfiction writing at Boston College, Johns Hopkins University, many other conferences and residencies. An ovarian cancer survivor, Kennedy lives in Somerville, Massachusetts with her partner, Kevin Bruyneel, she lived with filmmaker Liz Canner, in a relationship she has described as similar to a Boston marriage. Kennedy's accomplishments have been recognized many times during her career, she has been the recipient of a National Endowment for the Arts fellowship in fiction, a Sonora Review fiction prize, a Smithsonian Fellowship for science writing. Spinsters The Exes Confessions of a Memory Eater Stripping Platforms: A Microwaved Cultural Chronicle of the 1970s Zine: How I Spent Six Years of My Life in the Underground and Finally... Found Myself... I Think Pagan Kennedy's Living: Handbook for Ageing Hipsters Black Livingstone: A True Tale of Adventure in the Nineteenth-Century Congo The First Man-Made Man: The Story of Two Sex Changes, One Love Affair, a Twentieth-Century Medical Revolution The Dangerous Joy of Dr. Sex and Other True Stories Inventology: How We Dream Up Things That Change the World The Year's Best Fantasy and Horror Eighth Annual Collection The Best Creative Nonfiction Volume 2 Elvis's Bathroom Official website Website for The Dangerous Joy of Dr. Sex Profile of Kennedy

Pima County Natural Resources, Parks and Recreation

Pima County Natural Resources and Recreation is the agency within Pima County, Arizona that manages the natural resources and recreation offerings within Pima County including Tucson, AZ. The agency was established by the county as the Parks and Recreation Department in 1947 with the intended goal of serving "urban and rural residents and guests by providing leisure-time destinations and services." NRPR manages 51 parks with the majority located near Tucson. Ajo's parks include Ajo Regional Park, E. S. Bud Walker Park, Forrest Rickard Park, Palo Verde II Park. Green Valley's parks include Canoa Ranch; the Loop Cañada del Oro River Park Harrison Greenway Julian Wash Greenway Pantano River Park Rillito River Park Santa Cruz River Park 36th Street Trailhead Abrego Trailhead Agua Caliente Hill South Trailhead Avenida de Suzenu Trailhead Bear Canyon Trailhead Camino de Oeste Trailhead Campbell TrailheadCentral Arizona Project Trailhead Colossal Cave Road Trailhead David Yetman West Trailhead El Camino del Cerro Trailhead Explorer Trailhead Gabe Zimmerman Davidson Canyon Trailhead Gates Pass Trailhead Iris Dewhirst Pima Canyon Trailhead King Canyon Trailhead Richard Genser Starr Pass Trailhead Richard McKee Finger Rock Trailhead Sarasota Trailhead Sweetwater Preserve Trailhead Ventana Canyon Trailhead The NRPR has 13 community centers: Ajo Community Center Arivaca Community Center Catalina Community Center Centro Del Sur Community Center and Boxing Gym Continental Community Center Drexel Heights Community Center Ellie Towne Flowing Wells Community Center John A. Valenzuela Youth Center Littletown Community Center Mt. Lemmon Community Center Northwest YMCA Pima County Community Center Picture Rocks Community Center Robles Ranch Community Center The NRPR has 10 pools and 2 splash pads community centers: Ajo Pool Brandi Fenton Splash Pad Catalina Pool Flowing Wells Pool Kino Pool Los Niños Pool Manzanita Pool Park Picture Rocks Pool and Splash Pad Thad Terry Pool Wade McLean Pool Southeast Archery Range Southeast Clay Target Center Southeast Regional Park Shooting Range Tucson Mountain Park Archery Range Tucson Mountain Park Rifle and Pistol Range Virgil Ellis Shooting Range

Port Edwards (town), Wisconsin

Port Edwards is a town in Wood County, United States. The population was 1,446 at the 2000 census; the Village of Port Edwards is located to the northeast of and adjacent to the town. According to the United States Census Bureau, the town has a total area of 39.2 square miles, of which, 38.6 square miles of it is land and 0.6 square miles of it is water. The part of the town of Port Edwards within three miles of the Wisconsin River was in the "Indian strip," sold by the Menominee to the U. S. government in the 1836 Treaty of the Cedars. As such, it was surveyed early. In 1839 a crew working for the U. S. government surveyed what would become parts of Port Edwards, walking through the woods and crossing the river, measuring with chain and compass. In 1851 a different crew surveyed the section lines. For the six mile square that now contains Nekoosa and the village of Port Edwards, they gave this general description: The character of the Soil in this town is uniform; the Uplands are all pine barrens on a light Sandy Soil. the timber nearly all burned off by the yearly Indian fires.

The large pines, valuable for lumber, are all gone. The bottom lands tho somewhat better, are sandy & not sufficiently large to make them valuable. Inhabitants are scarce thin being a Single house at Pt. Bausse, a noted place for refitting rafts after passing the rapids before their final departure for the Mississippi, & a French hamlet on Section 1. On the whole it may be said of this town that for timber it is nearly worthless; the Islands in the river are all overflowed & are neither valuable for size, soil, or timber & were therefore not meandered. Port Edwards was established in 1874, taking its name from the village of the same name within its borders; as of the census of 2000, there were 1,446 people, 526 households, 399 families residing in the town. The population density was 37.4 people per square mile. There were 555 housing units at an average density of 14.4 per square mile. The racial makeup of the town was 91.01% White, 0.14% Black or African American, 5.26% Native American, 0.83% Asian, 2.07% from other races, 0.69% from two or more races.

4.56 % of the population were Latino of any race. There were 526 households out of which 35.9% had children under the age of 18 living with them, 64.1% were married couples living together, 8.7% had a female householder with no husband present, 24.1% were non-families. 20.5% of all households were made up of individuals and 6.3% had someone living alone, 65 years of age or older. The average household size was 2.75 and the average family size was 3.17. In the town, the population was spread out with 30.7% under the age of 18, 6.1% from 18 to 24, 29.4% from 25 to 44, 23.9% from 45 to 64, 10.0% who were 65 years of age or older. The median age was 36 years. For every 100 females, there were 103.4 males. For every 100 females age 18 and over, there were 102.4 males. The median income for a household in the town was $43,804, the median income for a family was $52,604. Males had a median income of $41,736 versus $26,250 for females; the per capita income for the town was $20,020. About 4.2% of families and 6.1% of the population were below the poverty line, including 6.8% of those under age 18 and 11.7% of those age 65 or over.

John Edwards and politician 1852 plat map of the six mile square that covers eastern Port Edwards and western Saratoga 1879 plat map of same 1896 plat map of same 1909 plat map 1928 plat map 1956 plat map of the six mile square that covers eastern Port Edwards and western Saratoga For other plats of western Port Edwards, see external links under Cranmoor

Bone morphogenetic protein 5

Bone morphogenetic protein 5 is a protein that in humans is encoded by the BMP5 gene. The protein encoded by this gene is member of the TGFβ superfamily. Bone morphogenetic proteins are known for their ability to induce cartilage development. BMP5 may play a role in certain cancers. Like other BMP's BMP5 is inhibited by noggin, it is expressed in the trabecular meshwork and optic nerve head and may have a role in the development and normal function. It is expressed in the lung and liver; this gene encodes a member of the bone morphogenetic protein family, part of the transforming growth factor-beta superfamily. The superfamily includes large families of differentiation factors. Bone morphogenetic proteins were identified by an ability of demineralized bone extract to induce endochondral osteogenesis in vivo in an extraskeletal site; these proteins are synthesized as prepropeptides and processed into dimeric proteins. This protein may act as an important signaling molecule within the trabecular meshwork and optic nerve head, may play a potential role in glaucoma pathogenesis.

This gene is differentially regulated during the formation of various tumors. Human BMP5 genome location and BMP5 gene details page in the UCSC Genome Browser; this article incorporates text from the United States National Library of Medicine, in the public domain