In geometry, an icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, 60 identical edges, each separating a triangle from a pentagon; as such it is one of the Archimedean solids and more a quasiregular polyhedron. An icosidodecahedron has icosahedral symmetry, its first stellation is the compound of a dodecahedron and its dual icosahedron, with the vertices of the icosidodecahedron located at the midpoints of the edges of either, its dual polyhedron is the rhombic triacontahedron. An icosidodecahedron can be split along any of six planes to form a pair of pentagonal rotundae, which belong among the Johnson solids; the icosidodecahedron can be considered a pentagonal gyrobirotunda, as a combination of two rotundae. In this form its symmetry is D5d, order 20; the wire-frame figure of the icosidodecahedron consists of six flat regular decagons, meeting in pairs at each of the 30 vertices.

The icosidodecahedron has 6 central decagons. Projected into a sphere, they define 6 great circles. Buckminster Fuller used these 6 great circles, along with 15 and 10 others in two other polyhedra to define his 31 great circles of the spherical icosahedron. Convenient Cartesian coordinates for the vertices of an icosidodecahedron with unit edges are given by the permutations of: where φ is the golden ratio, 1 + √5/2; the icosidodecahedron has four special orthogonal projections, centered on a vertex, an edge, a triangular face, a pentagonal face. The last two correspond to the A2 and H2 Coxeter planes; the surface area A and the volume V of the icosidodecahedron of edge length a are: A = a 2 = a 2 ≈ 29.3059828 a 2 V = 14 + 17 φ 3 a 3 = 45 + 17 5 6 a 3 ≈ 13.8355259 a 3. The icosidodecahedron can be represented as a spherical tiling, projected onto the plane via a stereographic projection; this projection is conformal, preserving angles but not lengths. Straight lines on the sphere are projected as circular arcs on the plane.

The icosidodecahedron is a rectified dodecahedron and a rectified icosahedron, existing as the full-edge truncation between these regular solids. The icosidodecahedron contains 12 pentagons of the dodecahedron and 20 triangles of the icosahedron: The icosidodecahedron exists in a sequence of symmetries of quasiregular polyhedra and tilings with vertex configurations 2, progressing from tilings of the sphere to the Euclidean plane and into the hyperbolic plane. With orbifold notation symmetry of *n32 all of these tilings are wythoff construction within a fundamental domain of symmetry, with generator points at the right angle corner of the domain; the icosidodecahedron is related to the Johnson solid called a pentagonal orthobirotunda created by two pentagonal rotunda connected as mirror images. The icosidodecahedron can therefore be called a pentagonal gyrobirotunda with the gyration between top and bottom halves; the truncated cube can be turned into an icosidodecahedron by dividing the octagons into two pentagons and two triangles.

It has pyritohedral symmetry. Eight uniform star polyhedra share the same vertex arrangement. Of these, two share the same edge arrangement: the small icosihemidodecahedron, the small dodecahemidodecahedron; the vertex arrangement is shared with the compounds of five octahedra and of five tetrahemihexahedra. In four-dimensional geometry the icosidodecahedron appears in the regular 600-cell as the equatorial slice that belongs to the vertex-first passage of the 600-cell through 3D space. In other words: the 30 vertices of the 600-cell which lie at arc distances of 90 degrees on its circumscribed hypersphere from a pair of opposite vertices, are the vertices of an icosidodecahedron; the wire frame figure of the 600-cell consists of 72 flat regular decagons. Six of these are the equatorial decagons to a pair of opposite vertices, they are the six decagons which form the wire frame figure of the icosidodecahedron. In the mathematical field of graph theory, a icosidodecahedral graph is the graph of vertices and edges of the icosidodecahedron, one of the Archimedean solids.

It has 30 vertices and 60 edges, is a quartic graph Archime

William Henry White was a British architect, as well as 18 years secretary of the Royal Institute of British Architects.. On the completion of his articles in London with George Morgan, he crossed the Channel, after a short term in the office of a French architect, established himself in Paris, he met influential clients, who commissioned him renovation of old chateaus including Chateau de Bizy and Chateau de Martinvast. At the time, White received an architect pupil, Charles Alfred Chastel de BoinvileAfter the Franco-Prussian War broke out, White returned to the Britain and found new job in India through his father connection, where he entered the Public Works Department of the Indian Government, he designed several important buildings, such as the Court of Small Causes at Calcutta, the Monument to Chief Justice Norman, the Presidency College. After travelling in India and on the Continent, White returned to London and took up journalistic work, contributing his articles to The Builder. About this time he was appointed the Examiner in Architecture at the Royal Indian Engineering College, Cooper’s Hill, a post be occupied for about two years.

The Secretaryship of this Royal Institute became vacant in 1878 through the retirement of Charles Eastlake, the present Keeper and Secretary of the National Gallery. White gained the post, served his time eighteen years—an era in the progress of the Institute marked by increased influence at home and abroad, a more extended system of administration. A glance at any of the official publications at the period when White entered upon his duties, put in comparison with any recent number of the JOURNAL, or a volume of the TRANSACTIONS issued till within the last three years, will suffice to show the amount of increased responsibility imposed upon the Secretary as Editor of all the Institute publications. In 1892, he published "The Architect and his artists, an essay to assist the public in considering the question is architecture a profession or an art" in reply to "Architecture, a Profession or an Art" edited by Norman Shaw and T. G. Jackson; this had been part of the course of events which resulted in the passing of the Architects Acts, 1931 to 1938 which established the statutory Register of Architects and monopolistic restrictions on the use of the vernacular word "architect", imposed with threat of penalty on prosecution for infringement.

The keeping of the Register of Architects is now governed by the Architects Act 1997, the name of the body responsible for the Register has been changed from the Architects' Registration Council of the United Kingdom to the Architects Registration Board. 1. Dictionary of British Architects, 1834-1914, Vol. 2, p.977. 2. Obituary William H. White, Journal of Royal Institute of British Architects, 1897, p.11-15

In 1980, several new characters were added to the British television soap opera Coronation Street: they were Martin Cheveski, Arnold Swain and Frankie Baldwin. None of them stayed in the show for more than a few months. Martin Cheveski was introduced in 1980 as Elsie Tanner's second grandson. Previous scripts had eststablished that Elsie only had 19-year-old Paul. However, despite this decision the show cast an older actor in the role, with Daran Little stating in his book The Life and Times of Coronation Street that this damaged the character's popularity as'Jonathan Caplan never managed to look 16'. Little commented on the irony of producers opting not to introduce Elsie's existing 19-year-old grandson, stating'the actor would have been perfect for the part'. Martin was born in Canada in 1964, his parents Ivan and Linda, older brother Paul, had emigrated there in 1961 but the family returned to England in 1966 Birmingham, where Martin went to school. After leaving school at sixteen, Martin got into rows with Ivan.

After a fall-out, Martin decided to stay with his grandma Elsie Tanner in Weatherfield. He made his own way there, arriving unannounced at Elsie's door on 16 June 1980. Elsie agreed to Martin living there, with Linda's approval; as it transpired, Martin had made the right decision, at least on the employment front. He was good with his hands, Len, who owned the local Builder's Yard, was a close friend of Elsie's and agreed to take Martin on as an apprentice; this upset the yard's labourer Eddie Yeats as there wasn't enough work at the yard for the three of them, unsurprisingly it was Eddie who faced the chop, having unsuccessfully tried to put Martin off the job. In August, Martin was repairing the water boiler at Baldwin's Casuals when he took a shine to the new trainee Karen Oldfield. Karen returned his affections and they went to a dance together, they soon fell for each other but a complication arose in the form of Karen's protective father, who barred Karen from seeing Martin when Martin got Karen drunk on Elsie's gin while entertaining her at No.11 in Elsie's absence.

Martin arranged to meet Karen despite the ban but to his shock it was Mr. Oldfield who showed up, to warn him off Karen personally. Karen was still willing to see Martin, but as Elsie wouldn't let them use No.11, Martin used the yard as a meeting place, with them seeing each other there on nights. The relationship continued. In October, the pair got, they were caught together at the yard by the police, resulting in Oldfield finding out that they were still together. With Oldfield threatening Martin with court action, Martin decided to return to Birmingham, deciding that if he couldn't see Karen there was nothing for him in Weatherfield; this surprised Oldfield, who agreed to let him see Karen - but warned him about getting her drunk again. At Christmas, Martin faced a complication as Karen wanted him to celebrate the day with her instead of his family, threatened to leave him otherwise. Martin left for Birmingham but came back deciding to be with Karen after all, but interrupted a date between Karen and Paul Sidall, shoved Paul across a table at the Rovers.

Martin realised he'd gone too far and risked pushing her closer to Paul, but after getting an idea from Elsie, bought an engagement ring and proposed to Karen, hoping that a big gesture would show his commitment to her and thus sort out their problems. Karen accepted but after consideration returned the ring, telling him they were too young, she finished with him. Though it was New Year's Eve, Martin packed his things and returned to Birmingham, telling Elsie he was swearing off girls. Arnold Henry Swain was a pet shop owner who bigamously married Emily Bishop in 1980, he died in a mental hospital in 1981, after unsuccessfully trying to coerce Emily into joining him in a suicide pact. Arnold was a man who knew what he wanted from life but brushed over the mistakes he made a little too easily. One of his tendencies was to disregard other people's feelings or push them to get his way - something which meant he wasn't always popular but some forgave him as he was charming. Arnold married Margaret in 1965 and they honeymooned in Shanklin, on the Isle of Wight.

The union did not work out as Arnold walked out on Margaret after the honeymoon, but told other people that she had left him. They stayed married. By 1980, Arnold owned a pet shop and ran it with his spinster sister Flora, who he lived with. In April of that year, he met widow Emily Bishop when he hired the Coronation Street Secretarial Bureau to do the shop's books. Arnold took a shine to Emily and asked her out - an invitation the shy Emily accepted when she found a poem Arnold had written which impressed her. Emily hadn't been with anyone since her husband Ernest died two years and hadn't expected another man to take an interest in her but was flattered and kept on seeing Arnold, which delighted him. In fact, Emily was so surprised at first that she worried he might be interested in her finances, but her fears were quelled when Deirdre Langton checked Arnold's finances and learned that he had his money well invested. A few weeks - a short time by any standards - Arnold proposed to Emily. Emily turned him down, feeling he was rushing her, but Arnold was persist