Josef Trajber was an Austrian speedcuber. A successful author of a Rubik's Cube book, he represented Austria in the 1982 World Rubik's Championship. He is also the inventor of a Rubik's Cube shape variant known as Trajber's Octahedron.
In 1982 Trajber was 25-years-old and was a computer programmer from Vienna. Although he previously had a personal best time of 29 seconds, at the World Rubik's Cube Championship 1982 he finished in 19th and last place with a best time in round one of 50.16 seconds. David Singmaster notes that he was one of the few contestants using the Layer by Layer method instead of the (then) more popular Corners First method.
Trajber was the best-selling author of the 1981 German-language book Der Würfel (The Cube) which was published in at least four editions with different publishers and different titles but an identical number of pages. The book was translated into several other languages, including Dutch (De Tover dobbelsteen), French (Le Rubik's Cube), Serbo-Croat (Rubikova kocka), Spanish (El cubo de Rubik), and Swedish (Trolltärningen). In 1988 he also published a German-language book on Rubik's Clock.
Trajber is the inventor of "Trajber's Octahedron" - one of the shape-variants of the original 3x3x3 which were produced for a very limited time in the 1980s. It is formed by truncating a Cube until none of the Cube faces are left, producing an Octahedron. According to David Singmaster, who saw a prototype in 1981:
The 8 triangular faces are coloured with 8 colours. A face centre of the Cube is now a corner of the Octahedron, and has four colours on it. By adjusting the relative spacing of the Cube's bisecting planes so the edge pieces are no longer cubical, we can make it so that a corner of the Cube is now a triangular face centre of the Octahedron with only one colour on it. ... Its solution is similar to the cube, but requires some new insights. It has 8!·12!·212·46 / 2·2·2 = 4.1 × 1019 = 40 50301 90700 29824 patterns.
In 1982 Singmaster further stated:
Trajber's Octahedron has been produced in Taiwan, in two forms. The other form has the vertex pieces slightly truncated.
Original 1980s versions of this puzzle are very rare and sell for high prices. However since around 2010, new versions have been produced and are currently available.