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= = = Great dodecicosahedron = = =

In geometry, the great dodecicosahedron (or great dodekicosahedron) is a nonconvex uniform polyhedron, indexed as U. Its vertex figure is a crossed quadrilateral.

It has a composite Wythoff symbol, 3 5/3 (3/2 5/2) |, requiring two different Schwarz triangles to generate it: (3 5/3 3/2) and (3 5/3 5/2). (3 5/3 3/2 | represents the "great dodecicosahedron" with an extra 12 {10/2} pentagons, and 3 5/3 5/2 | represents it with an extra 20 {6/2} triangles.)

Its vertex figure "6.10/3.6/5.10/7" is also ambiguous, having two clockwise and two counterclockwise faces around each vertex.

It shares its vertex arrangement with the truncated dodecahedron. It additionally shares its edge arrangement with the great icosicosidodecahedron (having the hexagonal faces in common) and the great ditrigonal dodecicosidodecahedron (having the decagrammic faces in common).

There is some controversy on how to colour the faces of this polyhedron. Although the common way to fill in a polygon is to just colour its whole interior, this can result in some filled regions hanging as membranes over empty space. Hence, the "neo filling" is sometimes used instead as a more accurate filling. In the neo filling, orientable polyhedra are filled traditionally, but non-orientable polyhedra have their faces filled with the modulo-2 method (only odd-density regions are filled in).

= = = Tony Award for Best Direction of a Play = = =

The Tony Award for Best Direction of a Play has been given since 1960. Before 1960 there was only one award for both play direction and musical direction, then in 1960 the award was split into two categories: "Dramatic" and "Musical". In 1976 the Dramatic category was renamed to Play. For pre-1960 direction awards please reference Tony Award for Best Director.

Only 6 women have won this award:

= = = Great rhombidodecahedron = = =

In geometry, the great rhombidodecahedron is a nonconvex uniform polyhedron, indexed as U. Its vertex figure is a crossed quadrilateral.

It shares its vertex arrangement with the truncated great dodecahedron and the uniform compounds of 6 or 12 pentagonal prisms. It additionally shares its edge arrangement with the nonconvex great rhombicosidodecahedron (having the square faces in common), and with the great dodecicosidodecahedron (having the decagrammic faces in common).

There is some controversy on how to colour the faces of this polyhedron. Although the common way to fill in a polygon is to just colour its whole interior, this can result in some filled regions hanging as membranes over empty space. Hence, the "neo filling" is sometimes used instead as a more accurate filling. In the neo filling, orientable polyhedra are filled traditionally, but non-orientable polyhedra have their faces filled with the modulo-2 method (only odd-density regions are filled in).

= = = Inverted snub dodecadodecahedron = = =

In geometry, the inverted snub dodecadodecahedron (or vertisnub dodecadodecahedron) is a nonconvex uniform polyhedron, indexed as U. It is given a Schläfli symbol sr{5/3,5}.

Cartesian coordinates for the vertices of an inverted snub dodecadodecahedron are all the even permutations of

with an even number of plus signs, where

where τ = (1+)/2 is the golden mean and

α is the negative real root of τα−α+2α−α−1/τ, or approximately −0.3352090.

Taking the odd permutations of the above coordinates with an odd number of plus signs gives another form, the enantiomorph of the other one.

The medial inverted pentagonal hexecontahedron (or midly petaloid ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform inverted snub dodecadodecahedron.

= = = Great snub dodecicosidodecahedron = = =

In geometry, the great snub dodecicosidodecahedron (or great snub dodekicosidodecahedron) is a nonconvex uniform polyhedron, indexed as U. It has Coxeter diagram, and Schläfli symbol s{(5/3,5/2,3)}. It has the unusual feature that its 24 pentagram faces occur in 12 coplanar pairs.

It shares its vertices and edges, as well as 20 of its triangular faces and all its pentagrammic faces, with the great dirhombicosidodecahedron, (although the latter has 60 edges not contained in the great snub dodecicosidodecahedron). It shares its other 60 triangular faces (and its pentagrammic faces again) with the great disnub dirhombidodecahedron.

The edges and triangular faces also occur in the compound of twenty octahedra. In addition, 20 of the triangular faces occur in one enantiomer of the compound of twenty tetrahemihexahedra, and the other 60 triangular faces occur in the other enantiomer.

There is some controversy on how to colour the faces of this polyhedron. Although the common way to fill in a polygon is to just colour its whole interior, this can result in some filled regions hanging as membranes over empty space. Hence, the "neo filling" is sometimes used instead as a more accurate filling. In the neo filling, orientable polyhedra are filled traditionally, but non-orientable polyhedra have their faces filled with the modulo-2 method (only odd-density regions are filled in). In addition, overlapping regions of coplanar faces can cancel each other out. The difference between the fillings of this polyhedron is very slight, but still present.

= = = Great inverted snub icosidodecahedron = = =

In geometry, the great inverted snub icosidodecahedron (or great vertisnub icosidodecahedron) is a uniform star polyhedron, indexed as U. It is given a Schläfli symbol sr{5/3,3}, and Coxeter-Dynkin diagram . In the book "Polyhedron Models" by Magnus Wenninger, the polyhedron is misnamed "great snub icosidodecahedron", and vice versa.

Cartesian coordinates for the vertices of a great inverted snub icosidodecahedron are all the even permutations of

with an even number of plus signs, where

and

where τ = (1+)/2 is the golden mean and

ξ is the greater positive real solution to ξ−2ξ=−1/τ, or approximately 1.2224727.

Taking the odd permutations of the above coordinates with an odd number of plus signs gives another form, the enantiomorph of the other one.

The circumradius for unit edge length is

where formula_2 is the appropriate root of formula_3. The four positive real roots of the sextic in formula_4

are the circumradii of the snub dodecahedron ("U"), great snub icosidodecahedron ("U"), great inverted snub icosidodecahedron ("U"), and great retrosnub icosidodecahedron ("U").

The great inverted pentagonal hexecontahedron (or petaloidal trisicosahedron) is a nonconvex isohedral polyhedron. It is composed of 60 self-intersecting pentagonal faces, 150 edges and 92 vertices.

It is the dual of the uniform great inverted snub icosidodecahedron.

= = = Prajavani = = =

Prajavani (Kannada for "Voice of the People") is a leading Kannada-language broadsheet daily newspaper published in Karnataka, India. Having a readership of over 2.01 million, it is one of the largest circulated newspapers in the state.

Prajavani was founded in 1948 in Bangalore by K.N. Guruswamy. The Printers (Mysore) Private Limited, the company which owns the newspaper, continues to be privately held by members of the founding family.

Prajavani (PV) has a history of being a politically independent newspaper, although it tends to opine with a liberal tilt. It is known for espousing the causes of Dalits, encouraging women's empowerment and taking pro-poor positions on economic issues. It has managed to maintain an independent position, despite an increasingly polarized media landscape in Karnataka. Prajavani uses the tagline "the most trusted Kannada daily newspaper", which appears below its masthead.

Prajavani was the leading Kannada newspaper for decades, until it was overtaken in circulation by "Vijaya Karnataka" (VK) in 2004. The gulf between PV and the upstart VK became huge for a while, but the two newspapers appear to be competing much more closely as of 2014, with PV having significantly recovered ground according to industry numbers. Some analysts have also attributed this to the launch of Vijaya Vani, by the original owner of Vijaya Karnataka, Vijay Sankeshwar and his VRL Group, which has apparently eaten into the readership of "Vijaya Karnataka". Other regional competitors include "Udayavani", "Varthabharathi", "Kannada Prabha" and "Samyukta Karnataka".

= = = Snub icosidodecadodecahedron = = =

In geometry, the snub icosidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U.

As the name indicates, it belongs to the family of snub polyhedra.

Cartesian coordinates for the vertices of a snub icosidodecadodecahedron are all the even permutations of

with an even number of plus signs, where

and where τ = (1+)/2 is the golden mean and

ρ is the real solution to ρ=ρ+1, or approximately 1.3247180.

ρ is called the plastic constant.

Taking the odd permutations of the above coordinates with an odd number of plus signs gives another form, the enantiomorph of the other one.

The medial hexagonal hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform snub icosidodecadodecahedron.

= = = Herman, Count of Aversa = = =

Herman (fl. c. 1050) was the son of Rainulf Trincanocte, count of Aversa (1045–1048), whom he succeeded. He was only an infant then and he was put under the regency of his father's cousin Richard. Within two years, he had disappeared from the scene and Richard was count. His fate is a mystery, though it is not hard to imagine that, as an obstacle to power, he was disposed of in the most efficient manner.

= = = 103rd Street station (IRT Broadway–Seventh Avenue Line) = = =

103rd Street is a local station on the IRT Broadway–Seventh Avenue Line of the New York City Subway. Located at the intersection of 103rd Street and Broadway on the Upper West Side of Manhattan, within Manhattan Valley, it is served by the 1 train at all times.

Operation of the first subway began on October 27, 1904, with the opening of the original 28 stations of the New York City Subway from City Hall to 145th Street on the West Side Branch including the 103rd Street station.

In 1948, platforms on the IRT Broadway–Seventh Avenue Line from 103rd Street to 238th Street were lengthened to to allow full ten-car express trains to platform. Previously the stations could only platform six-car local trains. The platform extensions were opened in stages. On April 6, 1948, the platform extension opened for stations from 103rd Street to Dyckman Street, with the exception of 125th Street.

In 2002, it was announced that 103rd Street would be one of ten subway stations citywide, as well as one of five on the IRT Broadway–Seventh Avenue Line, to receive renovations.

This station was part of the original subway, and has two side platforms and three tracks, the center one being an unused express track. The southbound local track is known as BB1 and the northbound one is BB4; the BB designation is used for chaining purposes along the Broadway–Seventh Avenue Line from 96th Street to 242nd Street and not in everyday speech. Although it cannot be accessed at 103rd Street, the center track is designated as M.

There is a mezzanine above the platforms, which contains the fare control area, as well as stairs to the street and both platforms.

This is the southernmost 3-track station on the line. South of the station, there are switches that connect the express track to either local track, with trains then being able to crossover to the rising express tracks from the IRT Lenox Avenue Line. Under 103rd Street, the dual express tracks serving the southern part of the line descend and curve to the east to form the IRT Lenox Avenue Line. They turn off of Broadway and onto 104th Street directly underneath this station. An emergency exit from the Lenox Avenue Line is located in the middle of the northbound platform.

The station has four entrance/exit stairs that serve both platforms:

A fifth, exit-only stair leads from the northbound platform to the SE corner of Broadway and 104th Street.

The 103rd Street station was one of the settings in the William S. Burroughs book "Junkie" and was briefly featured in the film "Black Swan".

= = = Small retrosnub icosicosidodecahedron = = =

In geometry, the small retrosnub icosicosidodecahedron (or retrosnub disicosidodecahedron or small inverted retrosnub icosicosidodecahedron) is a nonconvex uniform polyhedron, indexed as U. It is also called a retroholosnub icosahedron, ß{3/2,5}.

The 40 non-snub triangular faces form 20 coplanar pairs, forming star hexagons that are not quite regular. Unlike most snub polyhedra, it has reflection symmetries.

Its convex hull is a nonuniform truncated dodecahedron.

Cartesian coordinates for the vertices of a small retrosnub icosicosidodecahedron are all the even permutations of

where ϕ = (1+)/2 is the golden ratio and α = .

= = = Great retrosnub icosidodecahedron = = =

In geometry, the great retrosnub icosidodecahedron or great inverted retrosnub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U. It is given a Schläfli symbol sr{3/2,5/3}.

Cartesian coordinates for the vertices of a great retrosnub icosidodecahedron are all the even permutations of