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46-526: Built in 1934 by the Cox Fence Company, the original Dallas Sportatorium was constructed in the shape of an octagon , and seated approximately 10,000. Its inaugural wrestling event, promoted by Burt Willoughby, took place on December 9, 1935. Willoughby promoted wrestling at the Sportatorium until 1940, when the company was bought out by its former concessions manager, Ed McLemore. From 1948 until 1966,

92-606: A Juris Doctor (cum laude) from New York University School of Law where he was a Root-Tilden Scholar. After clerking for a New Jersey Supreme Court justice, Kelleher moved to Texas intending to start a law firm or a business. He was a partner in Oppenheimer, Rosenberg, Kelleher & Wheatley, 1969–1981. Kelleher and one of his law clients, Texas businessman Rollin King , created the concept with banker John Parker that later became Southwest Airlines. An often retold founding myth claimed

138-624: A corporate culture which made Southwest employees well known for taking themselves lightly but their jobs seriously. His culture-leadership was well-demonstrated in an arm-wrestling event in March 1992. Shortly after Southwest started using the "Just Plane Smart" motto, Stevens Aviation, who had been using "Plane Smart" for their motto, threatened a trademark lawsuit, which was resolved between Kelleher and Stevens Aviation CEO Kurt Herwald in an arm-wrestling match, now known as "Malice in Dallas". Kelleher lost

184-613: A number of octagonal churches in Norway . The central space in the Aachen Cathedral , the Carolingian Palatine Chapel , has a regular octagonal floorplan. Uses of octagons in churches also include lesser design elements, such as the octagonal apse of Nidaros Cathedral . Architects such as John Andrews have used octagonal floor layouts in buildings for functionally separating office areas from building services, such as in

230-482: A part of the new Trinity River Project , which has led to the renaming of Industrial Boulevard to Riverfront Boulevard. Octagon In geometry , an octagon (from Ancient Greek ὀκτάγωνον ( oktágōnon )  'eight angles') is an eight-sided polygon or 8-gon. A regular octagon has Schläfli symbol {8} and can also be constructed as a quasiregular truncated square , t{4}, which alternates two types of edges. A truncated octagon, t{8}

276-592: A partnership with wrestler Jack Adkisson , who was known in the ring as Fritz Von Erich and bought the Dallas/Fort Worth Wrestling Office, breaking away from Paul Boesch and the Houston Wrestling Office. In January 1968, McLemore started suffering a series of heart attacks and was no longer able to attend to the company's day-to-day business; he died on January 9, 1969, leaving Adkisson in charge. Adkisson's promotion, which became known in

322-415: A regular octagon is 135 ° ( 3 π 4 {\displaystyle \scriptstyle {\frac {3\pi }{4}}} radians ). The central angle is 45° ( π 4 {\displaystyle \scriptstyle {\frac {\pi }{4}}} radians). The area of a regular octagon of side length a is given by In terms of the circumradius R , the area is In terms of

368-471: A reputation for being uncomfortable and unsanitary (having inadequate heating and cooling facilities, rodent infestation problems and apparently a large chamber or pit in the foundation), the Dallas Sportatorium is nonetheless still remembered fondly for its intimate atmosphere, and is considered one of pro wrestling's most legendary venues. The land that had been occupied by the arena is slated to be

414-480: A right angle at the centre of the circle which connects its vertices. Its area can thus be computed as the sum of eight isosceles triangles, leading to the result: for an octagon of side a . The coordinates for the vertices of a regular octagon centered at the origin and with side length 2 are: Coxeter states that every zonogon (a 2 m -gon whose opposite sides are parallel and of equal length) can be dissected into m ( m -1)/2 parallelograms. In particular this

460-491: Is r16 and no symmetry is labeled a1 . The most common high symmetry octagons are p8 , an isogonal octagon constructed by four mirrors can alternate long and short edges, and d8 , an isotoxal octagon constructed with equal edge lengths, but vertices alternating two different internal angles. These two forms are duals of each other and have half the symmetry order of the regular octagon. Each subgroup symmetry allows one or more degrees of freedom for irregular forms. Only

506-408: Is a hexadecagon , {16}. A 3D analog of the octagon can be the rhombicuboctahedron with the triangular faces on it like the replaced edges, if one considers the octagon to be a truncated square. The sum of all the internal angles of any octagon is 1080°. As with all polygons, the external angles total 360°. If squares are constructed all internally or all externally on the sides of an octagon, then

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552-596: Is a zig-zag skew octagon and can be seen in the vertices and side edges of a square antiprism with the same D 4d , [2 ,8] symmetry, order 16. The regular skew octagon is the Petrie polygon for these higher-dimensional regular and uniform polytopes , shown in these skew orthogonal projections of in A 7 , B 4 , and D 5 Coxeter planes . The regular octagon has Dih 8 symmetry, order 16. There are three dihedral subgroups: Dih 4 , Dih 2 , and Dih 1 , and four cyclic subgroups : Z 8 , Z 4 , Z 2 , and Z 1 ,

598-446: Is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi. For the regular octagon , m =4, and it can be divided into 6 rhombs, with one example shown below. This decomposition can be seen as 6 of 24 faces in a Petrie polygon projection plane of the tesseract . The list (sequence A006245 in the OEIS ) defines the number of solutions as eight, by

644-517: The Intelsat Headquarters of Washington or Callam Offices in Canberra. The octagon , as a truncated square , is first in a sequence of truncated hypercubes : As an expanded square, it is also first in a sequence of expanded hypercubes: Herb Kelleher Herbert David Kelleher (March 12, 1931 – January 3, 2019) was an American billionaire airline businessman and lawyer. He

690-636: The Supreme Court of the United States in December 1970 and the Supreme Court of Texas in June 1971. The first flights finally took off on June 18, 1971. Reflecting back on that time Kelleher said, "I think my greatest moment in business was when the first Southwest airplane arrived after four years of litigation and I walked up to it and I kissed that baby on the lips and I cried." Kelleher's early involvement in

736-419: The apothem r (see also inscribed figure ), the area is These last two coefficients bracket the value of pi , the area of the unit circle . The area can also be expressed as where S is the span of the octagon, or the second-shortest diagonal; and a is the length of one of the sides, or bases. This is easily proven if one takes an octagon, draws a square around the outside (making sure that four of

782-733: The g8 subgroup has no degrees of freedom but can be seen as directed edges . The octagonal shape is used as a design element in architecture. The Dome of the Rock has a characteristic octagonal plan. The Tower of the Winds in Athens is another example of an octagonal structure. The octagonal plan has also been in church architecture such as St. George's Cathedral, Addis Ababa , Basilica of San Vitale (in Ravenna, Italia), Castel del Monte (Apulia, Italia), Florence Baptistery , Zum Friedefürsten Church (Germany) and

828-494: The hub-and-spoke scheduling system used by other airlines in favor of building point-to-point traffic, and focusing on secondary airports such as Chicago-Midway (instead of Chicago-O'Hare ), Dallas Love Field (instead of DFW ), and Orange County, California but later some hub flights were operated at airports, such as ATL , LAS, PHX, DEN, STL, and BWI and some major airports, like ORD, LGA, LAX, SFO, and DEN. The company he founded and built has consistently been named among

874-490: The 1990s when the arena was refurbished for the Global Wrestling Federation. During wrestling matches, the heel wrestlers came out of the northwest aisle, between sections B & C, while the babyfaces came out of the aisle on the southwest corner, or sections J & A. A broadcast studio was set up adjacent to the heel's locker room area; and an overhead section was later added for wrestling announcers to call

920-572: The GWF's demise, a succession of smaller promotions (including the NWA between 1995 and 1996) attempted to hold shows in the building, each of them running out of money and closing their doors after only a short time. However, it did gain one last bit of notoriety in March 1992 when Dallas-based Southwest Airlines held an arm-wrestling match between chairman Herb Kelleher and Kurt Herwald, chairman of Stevens Aviation, resulting from controversy over Southwest's use of

966-620: The Sportatorium was also the site of the Big D Jamboree , a weekly country music showcase similar in format to the Grand Ole Opry and Louisiana Hayride ; portions of the Jamboree were broadcast nationally on the CBS Radio Network . The Sportatorium was partially destroyed by fire on May 1, 1953, in what was rumored to be an act of arson by a rival wrestling promoter. It was quickly rebuilt at

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1012-450: The aging arena was seriously dilapidated by this time, was out of compliance with local building codes, and was often used as a shelter by homeless people who entered the building illegally. In late December 2001 a fire started inside the building. The flames quickly spread and caused major damage to the arena's upstairs offices. The fire proved to be the coup de grâce for the Sportatorium, its long-rumored demolition finally taking place in

1058-592: The arena for a time in 1989. After WCCW folded in 1990 due to dwindling attendance, fundamental changes in the wrestling industry and tragedies involving a number of its top stars (including all but one of the Von Erichs, Gino Hernandez , and Bruiser Brody ), the Sportatorium served as home base for the Global Wrestling Federation from 1991 to 1994 (billing itself for a time as the GlobalDome ). Following

1104-542: The board of directors in May 2008. The retirement of Barrett as president was announced at the same time, though the two would remain full-time employees for another five years. Kelleher ultimately stepped down as chairman on May 21, 2008. Immediately following, Southwest Airlines filled both the chairman and president positions with then-current CEO Gary C. Kelly , who had taken over the CEO position from Parker three years earlier. Kelleher

1150-603: The business plan was written out on a cocktail napkin in a San Antonio restaurant, though Kelleher and King have both stated that there was no literal cocktail napkin. They originally devised a very simple plan of connecting the Texas Triangle with low-cost air service, patterned largely on California's Pacific Southwest Airlines . After incorporating the company initially as "Air Southwest Co." in 1967, Kelleher and King faced four years of setbacks and legal challenges from competitors that culminated in winning key cases before

1196-406: The company was helping the company navigate legal concerns and as an advisor to the operation and later as general counsel. Lamar Muse was hired as CEO, but after struggles between Muse and King escalated over the next several years, Muse resigned in 1978. Kelleher was installed as chairman of the board in March of that year and the board appointed him as temporary CEO until hiring Howard Putnam as

1242-421: The early 1980s as World Class Championship Wrestling and featured his sons as its top stars, was the most famous and successful wrestling federation to run regularly at the Dallas Sportatorium. The arena was configured with several ring aisles with the majority of the seats (mostly bleachers) set up on the east, south and west portions of the building. The north side of the building, best known as "Section D",

1288-509: The eight orientations of this one dissection. These squares and rhombs are used in the Ammann–Beenker tilings . A skew octagon is a skew polygon with eight vertices and edges but not existing on the same plane. The interior of such an octagon is not generally defined. A skew zig-zag octagon has vertices alternating between two parallel planes. A regular skew octagon is vertex-transitive with equal edge lengths. In three dimensions it

1334-426: The eight sides overlap with the four sides of the square) and then takes the corner triangles (these are 45–45–90 triangles ) and places them with right angles pointed inward, forming a square. The edges of this square are each the length of the base. Given the length of a side a , the span S is The span, then, is equal to the silver ratio times the side, a. The area is then as above: Expressed in terms of

1380-404: The formulas for their length: A regular octagon at a given circumcircle may be constructed as follows: A regular octagon can be constructed using a straightedge and a compass , as 8 = 2 , a power of two : The regular octagon can be constructed with meccano bars. Twelve bars of size 4, three bars of size 5 and two bars of size 6 are required. Each side of a regular octagon subtends half

1426-402: The last implying no symmetry. On the regular octagon, there are eleven distinct symmetries. John Conway labels full symmetry as r16 . The dihedral symmetries are divided depending on whether they pass through vertices ( d for diagonal) or edges ( p for perpendiculars) Cyclic symmetries in the middle column are labeled as g for their central gyration orders. Full symmetry of the regular form

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1472-424: The match, but was allowed to use the slogan in exchange for a $ 5,000 charitable donation and conceding Stevens' legal claim to the slogan. In March 2001, Kelleher stepped down as CEO and president of Southwest. He passed the CEO role onto James Parker and the president role to Colleen Barrett , although he remained chairman. In July 2007, Southwest announced that Kelleher would step down as chairman and resign from

1518-485: The match. On the Industrial Blvd side of the arena was the offices of Big Time Wrestling/World Class Championship Wrestling (WCCW). Jack Adkisson and his sons each shared office space in the arena. Others like David Manning, Gary Hart , Ken Mantell , Percy Pringle , Skandor Akbar and Chris Adams would also occupy the front offices of the arena. Eric Embry , who was the Sportatorium's lead booker, lived inside

1564-415: The midpoints of the segments connecting the centers of opposite squares form a quadrilateral that is both equidiagonal and orthodiagonal (that is, whose diagonals are equal in length and at right angles to each other). The midpoint octagon of a reference octagon has its eight vertices at the midpoints of the sides of the reference octagon. If squares are constructed all internally or all externally on

1610-504: The most admired companies in America in Fortune magazine's annual poll. Fortune has also called him perhaps the best CEO in America. Your employees come first. And if you treat your employees right, guess what? Your customers come back, and that makes your shareholders happy. Start with employees and the rest follows from that. —Herb Kelleher Kelleher's outrageous personality created

1656-544: The new CEO and president. In 1981, after Putnam left to head Braniff Airways , he was appointed the full-time CEO and president, positions he held for 20 years. Under Kelleher's leadership, Southwest succeeded by a strategy of offering low fares to its passengers, eliminating unnecessary services, using a single aircraft type (the Boeing 737 ) (except for use of the Boeing 727 and use of MD-80 by TranStar and 717 by AirTran), avoiding

1702-412: The regular octagon in terms of the side length a is and the inradius is (that is one-half the silver ratio times the side, a , or one-half the span, S ) The inradius can be calculated from the circumradius as The regular octagon, in terms of the side length a , has three different types of diagonals : The formula for each of them follows from the basic principles of geometry. Here are

1748-534: The same location as a rectangular venue (with a modified octagonal seating configuration similar to the original), and reopened on September 22 of that year, billed at the time as The Million-Dollar Sportatorium . The arena also hosted boxing events and concerts featuring up-and-coming rock stars over the years, very much in the same manner as its Los Angeles counterpart, the Grand Olympic Auditorium , did during that time frame. In late 1966, McLemore formed

1794-501: The sides of the midpoint octagon, then the midpoints of the segments connecting the centers of opposite squares themselves form the vertices of a square. A regular octagon is a closed figure with sides of the same length and internal angles of the same size. It has eight lines of reflective symmetry and rotational symmetry of order 8. A regular octagon is represented by the Schläfli symbol {8}. The internal angle at each vertex of

1840-404: The slogan "Just Plane Smart" (Stevens claimed that it infringed on its own "Plane Smart" slogan). The match was a publicity stunt designed to raise funds for charity. The Sportatorium fell into disuse in the late 1990s when local independent wrestling promotions, by now drawing crowds only in the low hundreds, elected to run their shows in dance halls and other smaller venues instead. In addition,

1886-519: The span, the area is Another simple formula for the area is More often the span S is known, and the length of the sides, a , is to be determined, as when cutting a square piece of material into a regular octagon. From the above, The two end lengths e on each side (the leg lengths of the triangles (green in the image) truncated from the square), as well as being e = a / 2 , {\displaystyle e=a/{\sqrt {2}},} may be calculated as The circumradius of

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1932-732: The spring of 2003. Before its implosion, Kevin Von Erich took off a bench-seat and a few items from the Sportatorium as souvenirs. Kevin took one final tour of the historic arena, which was featured in its famed DVD documentary Heroes of World Class , released in 2006. Exactly 10 years after the death of Kerry Von Erich , February 18, 2003, the "World Famous Sportatorium" Main Entrance sign was saved from demolition by wrestling announcer Doyle King, who retains possession of it to this day. It has been on display at several local wrestling reunions and some local Dallas Fort Worth wrestling events. Although it had

1978-506: The worlds of business and aviation during his life. Some of the most notable include: At Wesleyan he was a member of Delta Kappa Epsilon fraternity. On a blind date at a basketball game, he met Joan Negley who was a student at Connecticut College in New London . The two got married, and Joan was the person who introduced him to the state of Texas , which he also fell in love with, saying "The greatest business decision I ever made ...was

2024-474: Was given the title of chairman emeritus with an office at Southwest Airlines headquarters and he remained connected to the company until his death in 2019. In July 2010, Kelleher was appointed chair of the Federal Reserve Bank of Dallas board of directors for 2011. Kelleher's term expired in 2013. Previously, he had served as deputy chair. Kelleher was the recipient of over 100 awards and honors in

2070-557: Was the co-founder, later CEO , and chairman emeritus of Southwest Airlines until his death in 2019. Kelleher was born in Camden, New Jersey , on March 12, 1931, and raised in Audubon, New Jersey , where he graduated from Haddon Heights High School . He earned a bachelor's degree from Wesleyan University where he was an Olin Scholar and where his major was English and his minor philosophy, and

2116-436: Was used mostly for a small stage and media area for cameras and reporters, but at least 10 rows of seats were also set up between the main stage/ring and the wall. A United States flag was displayed on the wall of section D for most of the arena's existence, and was changed once when the 48-star U.S. flag was replaced with a 50-star U.S. flag in 1960. The flag was moved to the section C area in 1987, then later above section I in

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