If one were going to build a coherent mathematical model of the universe would it look something like this geometrical object? Antony Garrett Lisi not only claims that it does, but has many other theoretical physicists up in arms about his weird scientific objects. Lisi claims to be at the beginning of a revolution in the way we understand both objects and the universe. What if the universe itself could be represented by a mathematical object? Lisi proposes that the universe can be explained by an extraordinary mathematical object called E8, a complex shape described by a pattern of 248 points in eight dimensions, with a structure that, if written out as an equation in tiny print, would cover an area the size of Manhattan.
Whether he is right or not is another matter, but his theory predicts new particles that many in the scientific community hope will be validated within the next few years as the Large Hadron Collider becomes fully operational and at maximum capacity. As James Owen Weatherall commented on Scientific American "if the structure of the universe at the tiny scales of elementary particles does turn out to be described by E8, with its 248 sets of circles wrapping around one another in an exquisite pattern, twisting and dancing over spacetime in all possible ways, then we will have achieved a complete unification and have the satisfaction of knowing we live in an exceptionally beautiful universe." 
A Non-Technical Overview of Lisi's Theory:
Consider a wavy, two-dimensional surface, with many different spheres glued to the surface—one sphere at each surface point, and each sphere attached by one point. This geometric construction is a fiber bundle, with the spheres as the "fibers," and the wavy surface as the "base". A sphere can be rotated in three different ways: around the x-axis, the y-axis, or around the z-axis. Each of these rotations corresponds to a symmetry of the sphere. The fiber bundle connection is a field describing how spheres at nearby surface points are related, in terms of these three different rotations. The geometry of the fiber bundle is described by the curvature of this connection. In the corresponding quantum field theory, there is a particle associated with each of these three symmetries, and these particles can interact according to the geometry of a sphere.
In Lisi's model, the base is a four-dimensional surface—our spacetime—and the fiber is the E8 Lie group, a complicated 248-dimensional shape, which some mathematicians consider to be the most beautiful shape in mathematics. In this theory, each of the 248 symmetries of E8 corresponds to a different elementary particle, which can interact according to the geometry of E8. As Lisi describes it: "The principal bundle connection and its curvature describe how the E8 manifold twists and turns over spacetime, reproducing all known ﬁelds and dynamics through pure geometry."
The complicated geometry of the E8 Lie group is described graphically using group representation theory. Using this mathematical description, each symmetry of a group—and so each kind of elementary particle—can be associated with a point in a diagram. The coordinates of these points are the quantum numbers—the charges—of elementary particles, which are conserved in interactions. Such a diagram sits in a flat, Euclidean space of some dimension, forming a polytope, such as the 421 polytope in eight-dimensional space.
In order to form a theory of everything, Lisi's model must eventually predict the exact number of fundamental particles, all of their properties, masses, forces between them, the nature of spacetime, and the cosmological constant. Much of this work is still in the conceptual stage—in particular, quantization and predictions of particle masses have not been done. And Lisi himself acknowledges it as a work-in-progress: "The theory is very young, and still in development." 
Different levels of magnification of matter
Levels of magnification:
1. Macroscopic level - Matter
2. Molecular level
3. Atomic level - Protons, neutrons, and electrons
4. Subatomic level - Electron
5. Subatomic level - Quarks
6. E8 (mathematics)
The Science Hostel
Lisi also proposes an interesting take on a new type of science institute, a science hostel:
"The physical requirements for conducting scholarly research have changed dramatically with the rise of the internet. It is now viable for researchers with laptop computers to work autonomously -- with access to current articles and communication channels on par with the resources available at large universities. These new circumstances motivate the creation of a new kind of research enterprise: a Science Hostel. By providing places to live and work with other researchers, in beautiful locations, a Science Hostel could increase creative productivity and overall quality of life for scholars in the internet age." 
Wouldn't it be nice to have scholars, philosophers, scientists, artists, and poets all interacting in these science hostels, a sort of Platonic Academy of Adventure and Theory. One can imagine a new Socrates of Objects saying, "Surfs up, dude!"
1. A Geometric Theory of Everything: Deep down, the particles and forces of the universe are a manifestation of exquisite geometry By A. Garrett Lisi and James Owen Weatherall | Monday, November 29, 2010
2. An Exceptionally Simple Theory of Everything - From Wikipedia, the free encyclopedia
3. Antony Garrett Lisi (2008-07-06). "Science Hostel". Science Hostel. http://sifter.org/~aglisi//sh.html. Retrieved 2008-07-06.