# Frabjous

Frabjous
Fields: Geometry and Other
Image Created By: George W. Hart
Website: George W. Hart

Frabjous

Frabjous is a sculpture created by George W. Hart from laser cut aspen wood. The sculpture is constructed from elongated s-curve pieces that, when fitted together, create a swirling vortex.

# Basic Description

This is an 11-inch diameter sculpture made of laser-cut wood. It is assembled from thirty identical pieces. Each is an elongated S-shaped form, with two openings.

One of the pieces for Frabjous

It is similar geometrically to George W. Hart's piece Bouquet, but is a one-of-a-kind piece and is very different visually. The aspen is quite light in color but the laser-cut edges are a rich contrasting brown. The openings add nicely to the whirling effect. The appearance is very different as one moves around it. The name Frabjous comes from Lewis Carroll's poem Jabberwocky: "O frabjous day! Callooh! Callay!"1

Connect the two vertices with a rod

Frabjous is featured on the Museum of Mathematics "Math Monday". You can buy the pieces to create your very own copy in the museum shop, or there is a template for the pieces on George W. Hart's website. There are many helpful guides to constructing the sculpture on the internet.

# A More Mathematical Explanation

Note: understanding of this explanation requires: *Geometry

Frabjous has 20 points, forms 12 "faces" of a swirling pattern, and is in the shape of a great rhombic triacontahedron. The base shape of the piece is a dodecahedron. This information is useful in understanding how the sculpture was created.

To understand the creation of the sculpture, picture the dodecahedron in terms of a pentagon (now called the base pentagon) connected to five other pentagons by sharing a line with each one. Connect each

All of the rods collide

vertex of the base pentagon to the tip of the opposite pentagon. Do this with every vertex in the dodecahedron. Unfortunately, all of the rods intersect at some point near the center. Adding two curves to the rod, one near each side, prevent the rods from

colliding and gives an interesting star pattern when looked at from the correct angle. The two openings on either end of the S-piece appear to serve no purpose other than artistic pleasure.

An aerial view of Frabjous
Frabjous from another angle

# About the Creator of this Image

George W. Hart graduated with a B.S. in Mathematics from MIT (1977), a M.A. in Linguistics from Indiana University (1979), and a Ph.D. in Electrical Engineering and Computer Science from MIT (1987). He has designed several geometrical pieces of art around the world, as well as helping with North America’s only Museum of Mathematics. He has worked at the MIT Lincoln Laboratory and MIT Energy Laboratory as a computer scientist, and taught at Columbia University for eight years and briefly at Hofstra Universtiy. After two years as a visiting scholar associated with the computational geometry group in the Department of Applied Mathematics and Statistics at Stony Brook, he was a research professor in the Department of Computer Science at Stony Brook (2001-2010). He is the author of over sixty scholarly articles and conference papers.

# References

• Artifacture (2012) Solving the Frabjous Sculpture: Vimeo. http://vimeo.com/34192802
• Caroll, Lewis (1872) Jabberwocky. Through the Looking-Glass and What Alice Found There: Macmillian.