Hypergeometry is the esoteric art of folding space into shapes beyond the ken of humanity, a mystic practise codified by the great minds of the Titans and held a jealous secret by the Guild of Philosophers during the reign of the Autarchs. Those who mastered hypergeometry could create doorways between worlds, build palaces with myriad rooms that appeared from the outside to be merely the size of a coffin, and could even walk through solid objects as though they were but smoke.
The study of the mysteries of hypergeometry claimed many casualties, for those who seek to unpick the stitches of creation do so balanced upon a knife edge. The slightest mistake in hypergeometric calculations could cause strange and ghastly distortions of matter, creating monstrosities of perspective and dimension the sight of which turned even the most courageous man into a coward. Stories abound of hypergeometricians trapped at a right angle from everything around them, of men starving to death in small laboratories because though they walked day and night the door never grew any closer. It is believed that Planeyfolk are the descendants of such unfortunates, the race fathered by researchers who slipped through the cracks of Euclidean space into something new and strange.
Planeyfolk are living men and women who lack the third dimension of existence, living as flattened beings that appear much as animated pictures. They tend to keep themselves pressed against walls and other flat surfaces, as they find it difficult to control their bodies without support. Some Planeyfolk have normal human proportions, and could be mistaken for a real person unless they turned to one side and vanished. Others have rather more scrambled anatomy, their flat bodies distorted and moulded by strange vanishing points and unhallowed angles. Such creatures are kept well away from civilisation, as the very sight of them maddens the beholder and can cause blindness and even death.
The disposition of such beings is equally variable. Some are quite sane and intelligent, and are quite capable of conversing with those who live in three dimensions. Planeyfolk have acted as advisors for Autarchs and Hegemons, and even been celebrated poets and dancers. Some live to great ages, as the flow of time does not act upon them as it would on those who exist in three full dimensions. Other Planeyfolk however are driven totally insane by whatever it is they have seen beyond the bounds of normal dimensions, and they are variously shunned or worshipped as all madmen in Vaarn are.