Information: - Little Hagia Sophia ( Turkish : Kucuk Ayasofya Camii ) , formerly the Church of the Saints Sergius and Bacchus ( Greek : , Ekklsia ton Hagin Sergiou kai Bakchou en tois Hormisdou ) , is a former Eastern Orthodox church dedicated to Saints Sergius and Bacchus in Constantinople , converted into a mosque during the Ottoman Empire . This Byzantine building with a central dome plan was erected in the sixth century by Justinian , likely was a model for Hagia Sophia ( '' Holy Wisdom '' ) , and is one of the most important early Byzantine buildings in Istanbul . It was recognized at the time as an adornment to the entire city , and a modern historian of the East Roman Empire has written that the church , '' by the originality of its architecture and the sumptuousness of its carved decoration , ranks in Constantinople second only to St. Sophia itself '' . - Byzantine architecture is the architecture of the Byzantine Empire, also known as the Later Roman or Eastern Roman Empire. Byzantine architecture was mostly influenced by Roman and Greek architecture and later Sassanian and Islamic influences to an extent. This terminology is used by modern historians to designate the medieval Roman Empire as it evolved as a distinct artistic and cultural entity centered on the new capital of Constantinople rather than the city of Rome and environs. The empire endured for more than a millennium, dramatically influencing Medieval architecture throughout Europe and the Near East, and becoming the primary progenitor of the Renaissance and Ottoman architectural traditions that followed its collapse. - Hagia Sophia (from the ), "Holy Wisdom"; or "Sancta Sapientia") was a Greek Orthodox Christian patriarchal basilica (church), later an imperial mosque, and now a museum (Ayasofya Muzesi) in Istanbul, Turkey. From the date of its construction in 537 AD, and until 1453, it served as an Eastern Orthodox cathedral and seat of the Patriarch of Constantinople, except between 1204 and 1261, when it was converted by the Fourth Crusaders to a Catholic cathedral under the Latin Empire. The building was later converted into an Ottoman mosque from 29 May 1453 until 1931. It was then secularized and opened as a museum on 1 February 1935. Famous in particular for its massive dome, it is considered the epitome of Byzantine architecture and is said to have "changed the history of architecture". It remained the world's largest cathedral for nearly a thousand years, until Seville Cathedral was completed in 1520. Given the information above, choose from the list below the object entity that exhibits the relation 'architectural style' with the subject 'little hagia sophia'. Choices: - byzantine architecture - medieval architecture
byzantine architecture

(Question)
Information: - A triangular number or triangle number counts the objects that can form an equilateral triangle, as in the diagram on the right. The th triangular number is the number of dots composing a triangle with dots on a side, and is equal to the sum of the natural numbers from 1 to . The sequence of triangular numbers , starting at the 0th triangular number, is - In mathematics, a polygonal number is a number represented as dots or pebbles arranged in the shape of a regular polygon. The dots are thought of as alphas (units). These are one type of 2-dimensional figurate numbers. - The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The term can mean - A hexagonal number is a figurate number . The nth hexagonal number hn is the number of distinct dots in a pattern of dots consisting of the outlines of regular hexagons with sides up to n dots , when the hexagons are overlaid so that they share one vertex . The formula for the nth hexagonal number h_n = 2n ^ 2 - n = n ( 2n - 1 ) = ( ( 2n ) \ times ( ( 2n - 1 ) ) \ over 2 ) . \ , \ ! The first few hexagonal numbers ( sequence A000384 in OEIS ) are : 1 , 6 , 15 , 28 , 45 , 66 , 91 , 120 , 153 , 190 , 231 , 276 , 325 , 378 , 435 , 496 , 561 , 630 , 703 , 780 , 861 , 946 . Every hexagonal number is a triangular number , but only every other triangular number ( the 1st , 3rd , 5th , 7th , etc. ) is a hexagonal number . Like a triangular number , the digital root in base 10 of a hexagonal number can only be 1 , 3 , 6 , or 9 . The digital root pattern , repeating every nine terms , is '' 1 6 6 1 9 3 1 3 9 '' . Every even perfect number is hexagonal , given by the formula M_p 2 ^ ( p - 1 ) = M_p ( M_p + 1 ) / 2 = h -- ( ( M_p +1 ) / 2 ) = h -- ( 2 ^ ( p - 1 ) ) where Mp is a Mersenne prime . No odd perfect numbers are known , hence all known perfect numbers are hexagonal . For example , the 2nd hexagonal number is 2 3 = 6 ; the 4th is 4 7 = 28 ; the 16th is 16 31 = 496 ; and the 64th is 64 127 = 8128 . The largest number that can not be written as a sum of at most four hexagonal numbers is 130 . Adrien - Marie Legendre proved in 1830 that any integer greater than 1791 can be expressed in this way . Hexagonal numbers can be rearranged into rectangular numbers of size n by ( 2n 1 ) . Hexagonal numbers should not be confused with centered hexagonal numbers , which model the standard packaging of Vienna sausages . To avoid ambiguity , hexagonal numbers are sometimes called '' cornered hexagonal numbers '' . Given the information above, choose from the list below the object entity that exhibits the relation 'subclass of' with the subject 'hexagonal number'. Choices: - figurate number - mathematics - natural - number - polygon - polygonal number - sequence - sum - term - triangle
(Answer)
polygonal number