Disdyakis dodecahedron

In geometry, a disdyakis dodecahedron, is a Catalan solid with 48 faces and the dual to the Archimedean truncated cuboctahedron. As such it is face-transitive but with irregular face polygons, it superficially resembles an inflated rhombic dodecahedron—if one replaces each face of the rhombic dodecahedron with a single vertex and four triangles in a regular fashion one ends up with a disdyakis dodecahedron. More formally, the disdyakis dodecahedron is the Kleetope of the rhombic dodecahedron, it is the net of a rhombic dodecahedral pyramid. It has Oh octahedral symmetry, its collective edges represent the reflection planes of the symmetry. It can be seen in the corner and mid-edge triangulation of the regular cube and octahedron, rhombic dodecahedron. Seen in stereographic projection the edges of the disdyakis dodecahedron form 9 circles in the plane; the 9 circles can be divided into two groups of 3 and 6, representing in two orthogonal subgroups:, and: If its smallest edges have length a, its surface area and volume are A = 6 7 783 + 436 2 a 2 V = 1 7 3 a 3 The truncated cuboctahedron and its dual, the disdyakis dodecahedron can be drawn in a number of symmetric orthogonal projective orientations.

Between a polyhedron and its dual and faces are swapped in positions, edges are perpendicular. The disdyakis dodecahedron is one of a family of duals to the uniform polyhedra related to the cube and regular octahedron, it is a polyhedra in a sequence defined by the face configuration V4.6.2n. This group is special for having all number of edges per vertex and form bisecting planes through the polyhedra and infinite lines in the plane, continuing into the hyperbolic plane for any n ≥ 7. With an number of faces at every vertex, these polyhedra and tilings can be shown by alternating two colors so all adjacent faces have different colors; each face on these domains corresponds to the fundamental domain of a symmetry group with order 2,3,n mirrors at each triangle face vertex. First stellation of rhombic dodecahedron Disdyakis triacontahedron Kisrhombille tiling Great rhombihexacron—A uniform dual polyhedron with the same surface topology Williams, Robert; the Geometrical Foundation of Natural Structure: A Source Book of Design.

Dover Publications, Inc. ISBN 0-486-23729-X; the Symmetries of Things 2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, ISBN 978-1-56881-220-5 Eric W. Weisstein, Disdyakis dodecahedron at MathWorld. Disdyakis Dodecahedron Interactive Polyhedron Model

Draco in Chinese astronomy

The modern constellation Draco lies across one of the quadrants symbolized by the Black Tortoise of the North, Three Enclosures, that divide the sky in traditional Chinese uranography. The name of the western constellation in modern Chinese is 天龍座, meaning "the heaven dragon constellation"; the map of Chinese constellation in constellation Draco area consists of: Traditional Chinese star names Chinese constellations Draco – Chinese associations 香港太空館研究資源 中國星區、星官及星名英譯表 天象文學 台灣自然科學博物館天文教育資訊網 中國古天文 中國古代的星象系統

2018 Paris–Nice

The 2018 Paris–Nice was a road cycling stage race that took place between 4 and 11 March 2018 in France. It was the 76th edition of the Paris -- the sixth event of the 2018 UCI World Tour; the race was won on the final day by the Movistar Team's Marc Soler from Spain. Having started the final stage 37 seconds down on race leader Simon Yates in sixth place overall, Soler attacked around halfway into the stage along with compatriot David de la Cruz; as de la Cruz and Fraile contested stage honours, Soler finished third – acquiring four bonus seconds on the finish in addition to three gained at an earlier intermediate sprint – and with a 35-second gap to Yates and the remaining general classification contenders, it was enough to give Soler victory over Yates by four seconds. The podium was completed by Bahrain–Merida's Gorka Izagirre, moving ahead of teammate and brother Ion Izagirre due to bonus seconds won on the final day, 14 seconds behind Soler, who won the white jersey as best young rider.

Lotto–Soudal won the two other jerseys on offer in the race. With the performances of the Izagirre brothers, Bahrain–Merida were the winners of the teams classification; as Paris–Nice is a UCI World Tour event, all eighteen UCI WorldTeams were invited automatically and obliged to enter a team in the race. Four UCI Professional Continental teams competed. Paris–Nice is the first race for Groupama–FDJ under this nomenclature, as French insurance company Groupama signed a co-naming sponsorship deal with the team; the route of the 2018 Paris–Nice was announced on 9 January 2018. 4 March 2018 — Chatou to Meudon, 135 km 5 March 2018 — Orsonville to Vierzon, 187.5 km 6 March 2018 — Bourges to Châtel-Guyon, 210 km 7 March 2018 — La Fouillouse to Saint-Étienne, 18.4 km, individual time trial 8 March 2018 — Salon-de-Provence to Sisteron, 165 km 9 March 2018 — Sisteron to Vence, 198 km 10 March 2018 — Nice to Valdeblore La Colmiane, 175 km 11 March 2018 — Nice to Nice, 110 km In the 2018 Paris–Nice, four jerseys were awarded.

The general classification was calculated by adding each cyclist's finishing times on each stage. Time bonuses were awarded to the first three finishers on all stages except for the individual time trial: the stage winner won a ten-second bonus, with six and four seconds for the second and third riders respectively. Bonus seconds were awarded to the first three riders at intermediate sprints – three seconds for the winner of the sprint, two seconds for the rider in second and one second for the rider in third; the leader of the general classification received a yellow jersey. This classification was considered the most important of the 2018 Paris–Nice, the winner of the classification was considered the winner of the race; the second classification was the points classification. Riders were awarded points for finishing in the top ten in a stage. Unlike in the points classification in the Tour de France, the winners of all stages were awarded the same number of points. Points were won in intermediate sprints.

The leader of the points classification was awarded a green jersey. There was a mountains classification, for which points were awarded for reaching the top of a climb before other riders; each climb was categorised as either first, second, or third-category, with more points available for the more difficult, higher-categorised climbs. For first-category climbs, the top seven riders earned points; the leadership of the mountains classification was marked by a white jersey with red polka-dots. The fourth jersey represented the young rider classification, marked by a white jersey. Only riders born after 1 January 1993 were eligible. There was a classification for teams, in which the times of the best three cyclists in a team on each stage were added together. Official website