China, 1039-1054 AD., Northern Song dynasty, emperor Ren Zong, 1 Cash, Hartill 16.93 var.

China, Northern Song dynasty (960-1127 AD.), emperor: Ren Zong (Jen Tsung, Renzong) (reign 1022-63 AD.), reign title: Huang Song (1039-54 AD.), issued 1039-54 AD.,
1 Cash (25 mm / 3,62 g), cast, 8-pointed center hole (a "flower hole"),
Obv.: ( 皇 宋 通 寳 ) , Huang Song Tong Bao (Huang-Sung t'ung pao), seal script, top of Huang curved, Bao a rounded square,
Rev.: plain (8-pointed center hole).
Hartill 16.93 var. (8-pointed center hole) (rarity of the normal type: 15, very common) ; Schjöth 497 var. ; FD 904 var. .

A possible explanation for the non-square center hole based on info from http://primaltrek.com/flowerhole.html :

Most cast Chinese coins retained a familiar round shape with a square hole in the middle for more than two millennia. A small number of these coins, however, were released into circulation having holes with a more than four-sided square hole, they would have holes with"eight sides" (octagon) and, because their shape resembled flowers, the Chinese referred to them with such names as flower hole, rosette hole, or chestnut hole. Other coins would have holes with "six sides" (hexagon) and were said to have "turtle shell" holes. Westerners sometimes refer to these coins as having "star" holes.

For good or ill a significant number of them passed quality control from the Qin and early Western Han Dynasties beginning in 14 AD. during the reign of Wang Mang til the production of flower-holed coins declined sharply starting about the time of the reign of Emperor Xiao Zong (1163 - 1190 AD) of the Southern Song.
The large number of these coins that found their way into circulation during particularly the Tang and Song dynasties, which were renown for the high standards and quality of their coinage, would indicate that the flower hole was an intentional embellishment having important significance. Theories are that they may have identified a location where or time when the coins were cast or a symbolic function.
The appearance of flower holes on Chinese cash coins must have been intentional. They must have been created after the coins were removed from the molds during a final chiseling process. The coins were first broken off of cast "coin trees" (qianshu). Then, any excess metal that may have accidentally flowed into the center hole of the coin had to be removed with either a chisel for file. Finally, the coins were stacked onto a long metal rod. The rod was square so that once the coins, with their square center holes, were stacked onto it they could not rotate. The workers could then use a file to remove any metal sprue from the rims to make sure the coins were round.

Maybe the square metal rod where the coins were stacked onto in some cases seved as an internal file creating two or four additional sides to the center hole - intentionally or not.