Information: - Geometry (from the ; "geo-" "earth", "-metron" "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. - In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons) is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedra and the only one that has fewer than 5 faces. - A Heronian tetrahedron or perfect tetrahedron is a tetrahedron whose edge lengths , face areas and volume are all rational numbers . The faces must therefore all be Heronian triangles . A regular tetrahedron ( one with all faces being equilateral ) with all sides rational is not a Heronian tetrahedron because its face areas and volume are not rational numbers . 117 is the smallest possible length of the longest edge of a perfect tetrahedron with integral edge lengths . Its other edge lengths are 51 , 52 , 53 , 80 and 84 . - In geometry, a Heronian triangle is a triangle that has side lengths and area that are all integers. Heronian triangles are named after Hero of Alexandria. The term is sometimes applied more widely to triangles whose sides and area are all rational numbers. - In elementary geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices. The word polyhedron comes from the Classical Greek , as "poly-" (stem of , "many") + "-hedron" (form of , "base" or "seat"). Given the information above, choose from the list below the object entity that exhibits the relation 'named after' with the subject 'heronian tetrahedron'. Choices: - earth - geometry - hero of alexandria - mathematics - tetrahedron
hero of alexandria

Information: - The Russell Islands are two small islands (Pavuvu and Mbanika), as well as several islets, of volcanic origin, in the Central Province of Solomon Islands. They are located approximately northwest from Guadalcanal. The islands are partially covered in coconut plantations, and have a copra and oil factory at Yandina. Yandina also has basic services, including a store, post office, and airport. - Mborokua ( also known as Mary Island ) is an uninhabited , jungle - covered volcanic island 30 km west of the Russell Islands . It is occasionally visited by local fishermen , as well as by dive tours . - Solomon Islands is a sovereign country consisting of six major islands and over 900 smaller islands in Oceania lying to the east of Papua New Guinea and northwest of Vanuatu and covering a land area of . The country's capital, Honiara, is located on the island of Guadalcanal. The country takes its name from the Solomon Islands archipelago, which is a collection of Melanesian islands that also includes the North Solomon Islands (part of Papua New Guinea), but excludes outlying islands, such as Rennell and Bellona, and the Santa Cruz Islands. - Guadalcanal (indigenous name: "Isatabu") is the principal island in Guadalcanal Province of the nation of Solomon Islands in the south-western Pacific, northeast of Australia. Its European discovery was under the Spanish expedition of Alvaro de Mendana in 1568. The name comes from Guadalcanal, a village in the province of Seville, in Andalusia, Spain, birthplace of Pedro de Ortega Valencia, a member of Mendana's expedition. - Mbanika is an island in Solomon Islands; it is located in the Central Province and is the second largest of the Russell Islands. The principal settlement is Yandina. - Pavuvu is the largest of the Russell Islands in Central Province, Solomon Islands. It is located Northwest of Guadalcanal. The area is 129.19km. Given the information above, choose from the list below the object entity that exhibits the relation 'country' with the subject 'mborokua'. Choices: - australia - solomon islands - vanuatu
solomon islands