The Penrose triangle, also known as the tribar is an impossible
object. It was first created by the Swedish artist Oscar Reutersvärd in 1934.
The mathematician Roger Penrose independently devised and popularised it in the
1950s, describing it as "impossibility in its purest form". It is featured
prominently in the works of artist M. C. Escher, whose earlier depictions of
impossible objects partly inspired it.
The tribar can only exist as a 2-dimensional drawing, since it exploits the
overlapping of parallel lines drawn in different perspectives. It appears as a
solid object, made of three beams of square cross-section. All the beams are
mutually perpendicular, yet join to form a triangle.
M. C. Escher's lithograph Waterfall depicts a watercourse that flows in a zigzag
along the long sides of two elongated Penrose triangles, so that it ends up two
storeys higher than it began. The resulting waterfall, forming the short sides
of both triangles, drives a water wheel. Escher helpfully points out that in
order to keep the wheel turning some water must occasionally be added to
compensate for evaporation.
The concept can be extended to other polygons, making, for example the "Penrose
square", but the visual effect is not as striking.
It is possible to create a solid object which looks like a Penrose Triangle.
Such shapes can be either curved or have a break in them, but when viewed from a
certain angle give the illusion of the complete triangle.