Hyperbolic triangle the third angle. The triangle where two vertices are ideal points and the remaining angle is right, one of the first hyperbolic triangles (1818) described by Ferdinand Karl Schweikart. The triangle where all vertices are ideal points, an ideal triangle is the largest possible triangle in hyperbolic geometry because of the zero sum of the angles. The relations among the angles and sides are analogous to those of spherical trigonometry; the length scale for both spherical geometry and hyperbolic geometry can for example be defined as the length of a side of an equilateral triangle with fixed angles. The length
Penrose triangle angles at the vertices of the triangle they form. The beams may be broken, forming cubes or cuboids. This combination of properties cannot be realized by any three-dimensional object in ordinary Euclidean space. Such an object can exist in certain Euclidean 3-manifolds. There also exist three-dimensional solid shapes each of which, when viewed from a certain angle, appears the same as the 2-dimensional depiction of the Penrose triangle on this page (such as – for example – the adjacent image depicting a sculpture in Perth, Australia). The term "Penrose triangle" can refer to the 2-dimensional depiction or the impossible object