In geometry, a tetrahedron known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedra and the only one that has fewer than 5 faces; the tetrahedron is the three-dimensional case of the more general concept of a Euclidean simplex, may thus be called a 3-simplex. The tetrahedron is one kind of pyramid, a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. In the case of a tetrahedron the base is a triangle, so a tetrahedron is known as a "triangular pyramid". Like all convex polyhedra, a tetrahedron can be folded from a single sheet of paper, it has two such nets. For any tetrahedron there exists a sphere on which all four vertices lie, another sphere tangent to the tetrahedron's faces. A regular tetrahedron is one, it is one of the five regular Platonic solids. In a regular tetrahedron, all faces are the same size and shape and all edges are the same length.

Regular tetrahedra alone do not tessellate, but if alternated with regular octahedra in the ratio of two tetrahedra to one octahedron, they form the alternated cubic honeycomb, a tessellation. Some tetrahedra that are not regular, including the Schläfli orthoscheme and the Hill tetrahedron, can tessellate; the regular tetrahedron is self-dual. The compound figure comprising two such dual tetrahedra form a stellated octahedron or stella octangula; the following Cartesian coordinates define the four vertices of a tetrahedron with edge length 2, centered at the origin, two level edges: and Expressed symmetrically as 4 points on the unit sphere, centroid at the origin, with lower face level, the vertices are: v 1 = v 2 = v 3 = v 4 = with the edge length of 8 3. Still another set of coordinates are based on an alternated cube or demicube with edge length 2; this form has Coxeter diagram and Schläfli symbol h. The tetrahedron in this case has edge length 2√2. Inverting these coordinates generates the dual tetrahedron, the pair together form the stellated octahedron, whose vertices are those of the original cube.

Tetrahedron:, Dual tetrahedron:, For a regular tetrahedron of edge length a: With respect to the base plane the slope of a face is twice that of an edge, corresponding to the fact that the horizontal distance covered from the base to the apex along an edge is twice that along the median of a face. In other words, if C is the centroid of the base, the distance from C to a vertex of the base is twice that from C to the midpoint of an edge of the base; this follows from the fact that the medians of a triangle intersect at its centroid, this point divides each of them in two segments, one of, twice as long as the other. For a regular tetrahedron with side length a, radius R of its circumscribing sphere, distances di from an arbitrary point in 3-space to its four vertices, we have d 1 4 + d 2 4 + d 3 4 + d 4 4 4 + 16 R 4 9 = ( d 1 2 + d 2 2 + d 3 2 + d 4 2 4 + 2

Parliament of South Africa

The Parliament of South Africa is South Africa's legislature. The current twenty-seventh Parliament was first convened on 22 May 2019. From 1910 to 1994, members of Parliament were elected chiefly by the South African white minority; the first elections with universal suffrage were held in 1994. The predecessor of the Parliament of South Africa, before the 1910 Union of South Africa, was the bicameral Parliament of the Cape of Good Hope; this was composed of the House of the Legislative Council. It dated back to the beginnings of Cape independence in 1853 and was elected according to the multi-racial Cape Qualified Franchise system, whereby suffrage qualifications were applied to all males, regardless of race; the buildings of the Cape Parliament went on to house the Parliament of South Africa, after union. When the Union of South Africa was established in 1910, the Parliament was bicameral and consisted of the King or the Queen, the Senate, the House of Assembly; the King was represented by the Governor-General.

The Senate consisted of senators nominated by the four provinces, by the Governor-General for a period of ten years. The number of senators was changed from time to time; the Senate was chaired by a President of the Senate chosen by the senators from among themselves. The House of Assembly consisted of members; each MP represented an electoral district, most of them were elected on the basis of their political party. The number of constituencies and parliamentary seats was increased from time to time, in line with increases in the population; the House was chaired by a Speaker chosen by the MPs from among themselves. Only white men could be MPs; the franchise was granted to white men in all four provinces, to black men in the Cape Province and Natal, to Coloured men in the Cape Province – in all cases, the minimum age was 21 years. The composition of Parliament was changed by constitutional amendments from time to time: From 1930, white women had the vote, the right to serve as senators and MPs, on the same basis as white men.

In 1934, Parliament was declared "the sovereign legislative power in and over the Union". From 1937, black voters were separated from the other races – in the Senate they were represented by four elected senators, in the House of Assembly by three "native representative" MPs elected in separate black constituencies. From 1950, white voters in South West Africa, under South African administration at that time, were represented by four senators and six MPs. From 1957, Coloured voters were separated from the whites – in the Senate, they were represented by separate senators, in the House of Assembly by MPs elected in separate Coloured constituencies. To pass this amendment in the face of strong opposition, prime minister Johannes Strijdom had to enlarge the Senate and appoint enough pro-government senators to get the two-thirds majority he needed to force through the constitutional change. Representation of black voters was ended in 1960. Voting age was lowered from 21 to 18 in 1960. In a referendum held in 1960, a small majority of the white voters approved the conversion of the country from a Realm or Dominion of the British Commonwealth to a republic.

The Republic of South Africa was established in 1961. The only change made to the composition of the Parliament was the substitution of the State President for the Queen. A few significant changes were made later: Coloured representation was ended in 1968, leaving both the Senate and the House of Assembly representing white voters only. South West Africa ceased to be represented in Parliament from 1977; the Senate was abolished in 1981. A new Constitution, introduced in 1984, re-enfranchised the Coloured population and enfranchised the Indian population, it retained the existing House of Assembly for whites and established a House of Representatives to represent the Coloureds, a House of Delegates for the Indians, making Parliament a tricameral legislature. Blacks continued to be excluded; each house consisted of members elected to represent constituencies, plus a few additional members elected by the MPs, some nominated by the State President. Each house legislated on "own affairs" exclusive to its own race group, they legislated jointly on "general affairs" affecting all races.

In practice, the House of Assembly, which had more MPs than the other two houses combined, continued to dominate the legislature. Each house was chaired by a chairman elected by its members from among themselves, they were coordinated by a Speaker of Parliament, elected by the members of all three houses in a joint sitting. The existing House of Assembly, elected in 1981, was deemed to have been re-elected in 1984, to coordinate its term of office with those of the two new houses. However, this was overturned by the Supreme Court, a separate election had to be held for the House of Assembly in 1987; the House elected in 1987 was dissolved with the other houses in 1989. The black majority were still disfranchised, the new system lacked legitimacy among the Coloureds and Asians, many of whom boycotted elections. In a referendum held in 1992, 68.73% of voters approved the reform process that ended Apartheid. In late 1993, one of the last pieces of legislation passed by the tricameral Parlia

Ian Gibson (Scottish footballer)

Ian Gibson is a Scottish retired association football player. Gibson is most notable for being a regular first team player for Fitzroy United Alexander in the Victorian State League. Gibson is notable for playing South Melbourne Hellas in the National Soccer League's inaugural season in 1977. After his arrival from Scotland, Gibson began his football career in Melbourne, Australia signing with Fitzroy United Alexander in the fast growing Victorian State League for the 1973 season. Gibson made his debut for the club in the second round on 8 April 1973, against future National Soccer League club South Melbourne Hellas in a 0-1 loss at Olympic Park Stadium, his first goal for the club came four rounds on 5 May 1973, against Brunswick Juventus being the first the goal in 2-0 victory. In what was the club's first competitive home match at the Brunswick Street Oval on 13 April 1975, following the club coming to an agreement with the both the Fitzroy Lions and Fitzroy Cricket Club, Gibson scored the first goal in what would finish to be a 2-0 victory over South Melbourne Hellas in front of a near modern-day capacity crowd of 14'500 spectators in the memorable debut for the club.

In the four seasons Gibson spent with the North Fitzroy club, competing in the Victorian State League, Dockerty Cup, Ampol Cup and the State Preseason Challenge Cup, Gibson made a total of 89 appearances for Alexander, scoring 37 goals, including being an integral member of the 1975 state league championship victory, forming a famous link with fellow Scottish winger George Gillan. Gibson's last game for the club was on 12 September at the Brunswick Street Oval against Sunshine George Cross in a 1-1 draw. Following the assembly of the National Soccer League, Gibson along with fellow Scot and Fitzroy teammate & player-coach Jack Reilly were lured away from Brunswick Street Oval and joined rival Greek backed club South Melbourne Hellas on a one-year contract. Gibson made his debut for the club in the first round on 2 April 1977 against Sydney Olympic FC away in a 2-0 win, his first goal came in round 3 on 18 April 1977 against Melbourne based rivals Footscray JUST in a 2-2 draw. At the season's conclusion, Hellas disappointedly finished eleventh out of fourteen.

Gibson and former Fitzroy teammate George Gillan, who played for Alexander in the 1977 season with difficulty for a regular spot, both retired from the game professionally. As of 18 October 2016 With Fitzroy United Alexander: Victorian State League: Champions 1975