the fifth dimension

In 1993 the physicist Gerard 't Hooft put forward the holographic principle, which explains that the information about an extra dimension is visible as a curvature in a spacetime with one fewer dimensions. For example, holograms are three dimensional pictures placed on a two dimensional surface, which gives the image a curvature when the observer moves. Similarly, in general relativity, the fourth dimension is manifested in observable three dimensions as the curvature of path of a moving infinitesimal (test) particle. Hooft has speculated that the fifth dimension is really the spacetime fabric.

Source : WP

dimension b

PhysOrg forum - Aether Wave Theory


A complicated manifold - at Oberwolfach Mathematics Institute in Germany - by jmelli.
Some say it's a Boy's surface

De Gua 1

De Gua's theorem is a generalization of the Pythagorean theorem to three dimensions and named for Jean Paul de Gua de Malves. If a tetrahedron has a right angle corner (a corner like a cube), then the square of the area of the face opposite the right angle corner is the sum of the squares of the areas of the other three faces.
Just see WP, nothing to add for now.

stereogram

The Lake Palanskoye in northern Kamchatka was formed when a large landslide disrupted the drainage pattern, forming a natural dam. loucher sur l'image pour voir le relief. By NASA and sons.

One more dimension