The Visual Guide To Extra
Dimensions: Visualizing The Fourth
Dimension, Higher-Dimensional
Polytopes, And Curved
Hypersurfaces by Chris McMullen
Packed With Illustrations
Watch a tesseract unfold. See how the 3D cross section of a hypercube
changes as the hypercube rotates. View 4D wheels with axles with a
spherinder or cubinder structure. Imagine climbing a 4D staircase. Find
10 out of 120 dodecahedra of a hecatonicosachoron highlighted... all on
this visual tour of the fourth dimension. The book is much more visual
and conceptual than algebraic, yet it is detailed and technical, with the
intention of satisfying the needs of mathematically-minded readers familiar
with the fundamentals of algebra, geometry, and graphing.

Personal Review: The Visual Guide To Extra Dimensions:
Visualizing The Fourth Dimension, Higher-Dimensional
Polytopes, And Curved Hypersurfaces by Chris McMullen
* I was pleasantly surprised at the number and quality of diagrams
included in this book on the fourth dimension. Many diagrams were
instructive. They helped me visualize 4D objects, making the fourth
dimension seem somewhat less abstract.
* This was the first time that I can recall seeing 4D graphs of
hypersurfaces. This includes the cubinder, spherinder, hypercones,
hyperparaboloids, hyperhyperboloids, and hypertori. The following chapter,
A Hypothetical Hyperuniverse, describes possible 4D objects, machines,
and beings in terms of such hypersurfaces. Put together, I can almost
imagine a 4D world.
* There is also a very detailed chapter on objects with flat surfaces, called
polytopes (such as the hypercube). The hypercube is analyzed
extensively. The simplex and less common polytopes are also included.
There are some neat features here, such as diagrams that break down the
icositetrachoron.
* I've never found a book on the fourth dimension that suits me perfectly (I
can always find something that I would like to change), but there was much
that I enjoyed about this book. I highly recommend it to anyone who enjoys
thinking about 4D objects.
* I also recommend Rudy Rucker's classic introduction, The 4th
Dimension: Toward a Geometry of Higher Reality. Every fan of the fourth
dimension should also read Edwin Abbott's Flatland a Romance of Many
Dimensions - Edwin Abbott.
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