SCULPTURE DESIGNS and MATH MODELS by Carlo H. Séquin

Recent Work

"Octa-Boy-Surface" (July 2013) - FDM model 6" x 6" x 6" "Evolving Trefoil" (February 2013) -  10-foot diameter polyresin and

fiberglass sculpture, Missouri Western State University, St Joseph, MO.

"Music of the Spheres" (January 2013)",  - 10-foot tall bronze sculpture, Missouri Western State University, St Joseph, MO.

"Music of the Spheres" (January 2013)", (With Brent Collins and Steve Reinmuth) - 10-foot tall bronze sculpture, Missouri Western State University, St Joseph, MO.

"125 Terahedra in 25 projected 5-Cells", (November  2012) - FDM model, 7" x 7" x 7" -- Celebrating the 125th Anniversary of the American Mathematical Society.

"Double-Boy-Klein-Bottle" (October 2012) - FDM model, 7" x 7" x 7"

"Trefoil_Knottle_2 " (July 2012) - FDM model, 8" x  8" x 3"

"Pillar of Engineering" (installed May 2012), sponsored by Paul Suciu - 7-foot tall granite sculpture on the terrace of Sutardja Dai hall, UC Berkeley.

Work 2011-2012

"Zig-Zag Klein Bottle" (May 2012) - FDM model, 6" x  6" x 6" "TorusTransformation (April 2012) - FDM model, 7" x  6" x 5"

Hemi-Icosahedron (March 2012) - modular cardboard model, 10" diameter.

"Trefoil Knottle" (February 2012) - FDM model, 8" x  8" x 3"

"Kracy Kosmos of Klein Knottles", (February 2012) - Computer rendering.

"Klein Bottle of type K8JJ" (Jan 2012) - FDM model, 8" x  3" x 5"

Symmetrical Half-way Point for Torus Eversion (November 2011) - 3D-print by Zcorp, 6" x 5.5" x 4"

Lawson's Minimum-Energy Klein Bottle (December 2011) - FDM model, 9" x 6" x 4.5" -- 3rd prize at the AMS annual exhibition of Mathematical Art, Jan, 2012.

Gridded Cube Dissection Puzzle (December 2011) - FDM model, 5" x 5" x 5"

4-Finger Spiral Hyperboloid Dissection (December 2011) - FDM model, 2" x 2" x 4"

3-Finger Spiral Barrel Dissection (December 2011) - FDM model, 2" x 2" x 4"

Helicoidal Cube Trisection (November 2011) - FDM model, 3" x 3" x 3"

Helicoidal Tetrahedron Dissection (November 2011) - FDM model, 3" x 3" x 3"

Hemi-Icosahedron (July 2011) - FDM model, 4" diameter.

Work 2010-2011

Augmented Rhombicuboctahedron (June 2011) - Cardboard, 14" diameter. Augmented Pseudo-Rhombicuboctahedron (June 2011) - Cardboard, 14"

diameter.

Decremented Rhombicuboctahedron (June 2011) - Cardboard, 10" diameter.

"Wild and Wonderful Tori 2", (June 2011) - Computer rendering.

"Wild and Wonderful Tori 1", (March 2011) - Computer rendering.

"Internally Knotted Figure-8 Torus" (March 2011) - FDM model, 8" x 6" x 6".

"Evolving Trefoil" (January 2011) - FDM model, 7" diameter.

"Torus Knot-5-3 (version 2)" (August 2010) - Bronze, 16" tall. -- This sculpture won 2nd prize at the AMS annual exhibition of Mathematical Art, Jan, 2011.

Work 2009-2010

"Torus Knot (5,3)" (May 2010) - Bronze, 16" tall. "Knot7-7" (April 2010) - FDM model, 7" tall.

"Trefoil Standing on its Own Feet" (April 2010) - FDM model, 4" tall.

"Aurora Borealis" and "Aurora Australis" (February 2010) - bronze, 16" tall.

"Knot6-1" (February 2010) - FDM model, 5" tall.

Regular Map R3.5-{4,8} (January 2010) - paper, 4" diameter.

Regular Map R3.3-{3,12} (November 2009) - paper, 4" diameter.

"Scherk-Tower" (October 2009) - bronze, 10" tall, new surface.

"Dodecahedral Volution" (October 2009) - bronze, 5" tall, new surface.

"Poincaré Double_Lace" (September 2009) - canvas print, 18" square.

Regular Map R5.16-{20,20} (August 2009) - computer rendering.

"Aurora3 (master geometry)" (July 2009) - FDM, 16" tall.

Work 2008-2009

"Totem-4M" (June 2009) - bronze, 13" tall. "Cube-Volution-5" (June 2009) - bronze, 6" cube.

"Knot5-2" (May 2009) - FDM model, 5" tall.

"Various Knot models" (May 2009) - FDM models, 3-4" diameter.

"Regular Maps on Cube Frames" (April 2009) - Printed Paper, 4" cube.

"Escher-Tiles_3D" (March 2009) - FDM models, 2.5" each.

"Escher-Tiles_2.5D" (March 2009) - FDM models, 2.5" each.

"Hyperbolic Hexagon II" (February 2009) (With Brent Collins and Steve Reinmuth) - bronze, 30" diameter.

"Totem4M" (November 2008) - 11" tall FDM model.

"TorusKnot5-3" (November 2008) - FDM model, 6" tall.

Work 2007-2008

"Annual EuroGraphics Awards" (March 2008) - bronze, 8" tall. "MetroPolis" (January 2008) - assembly of FDM parts, 5" tall.

"Honeycomb" (January 2008) - assembly of FDM parts, 7" tall.

"Figure-8 Knot" (December 2007) - bronze, 9" tall.

"Totem4" (December 2007) - bronze, 11" tall.

"Chinese Button Knot" (December 2007) - bronze, 8" tall.

"SolarCircle" (November 2007) - 10-foot diameter polyresin and fiberglass ring; aka "Millennium Arc", Matt Ross Community Center, Overland Park, Kansas City.

10-segment ring-tile and 10-Torotile Lattice (November 2007) - 3" FDM model

6-segment ring-tile and 6-Torotile Lattic (November 2007) - 3" FDM model

4-segment ring-tile and 4-Torotile Lattic (October 2007) - 2" FDM model

"Recursive Figure-8 Knot" (October 2007) - 4" tall FDM model.

"Scherk-Tower" (September 2007) - bronze, 10" tall.

"Dodecahedral Volution" (September 2007) - bronze, 5" tall.

"The 4-dimensional 11-Cell" (August 2007) - Virtual computer model; -- selected for the "2008 Calendar of Mathematical Imagery".

"Totem4" (August 2007) - 11" tall FDM model.

"Hemi-Icosahedron" (July 2007) - 5" tall FDM model.

"Chinese Button Knot" (July 2007) - 6" tall FDM model.

"Quad_Rose" (July 2007) - 7" tall FDM model.

Work 2006-2007

"Ribbed Hemicube" (June 2007) - 5" tall FDM model. "Icosahedral Orbits" (May 2007) - 4" diam. FDM model.

"Dodecahedral Orbits" (May 2007) - 4" diam. FDM model.

"Twisted Scherk Tower" (February 2007) - 10" tall FDM model.

"Pax Mundi II" (January 2007) (With Brent Collins and Steve Reinmuth) - 10-foot tall bronze sculpture, H&R Block Headquarters, Kansas City. More installation pictures here -- and Pax Mundi II six months later.

"Trinity" - 'Reconfigurable Sculpture' (December 2006) - 3" tall FDM model.

"Spiral Surface 2" (November 2006) - 4.5" tall FDM model.

"Pax Mundi 2" (October 2006) - 7" tall FDM model for a 10-foot tall bronze sculpture to be installed in Kansas City.

"Trefoil Trisection" - Closed -- Open1 -- Open2 -- Open3 -- (September 2006) - FDM model, 5" diam.

"Separable Trefoil" - Closed -- Open -- (September 2006) - FDM model, 4" diam.

"High-Res. Lizard Tetrus" (August 2006) - Virtual computer model (with Pushkar Joshi) -- selected for the cover of the "2007 Calendar of Mathematical Imagery" of the American Mathematical Society.

Work 2005-2006

"Equatorial Weave on the {3,7} Tetroid" (June 2006) - FDM assembly, 6" tall. "Poincaré Double_Lace" (June 2006) - 2D print, 16" diam.

"Poincaré Lace" (June 2006) - 2D print, 16" diam.

"Poincaré FishDish" (May 2006) - 2D print, 16" diam.

"Tetrus with Bird Bas-Relief" (May 2006) - Virtual computer model (with Steven An).

"48Bird Tetrus" (April 2006) - Virtual computer model.

"Lizard Tetrus" (April 2006) - Virtual computer model.

"Ribbon Tetrus" (April 2006) - Fused deposition model, 4" tall.

"Tetroid assembled from 12 double heptagons" (March 2006) - FDM assembly, 3.5" tall.

"Tetroid with 56 Triangles, 8 colors" (February 2006) - FDM model, painted, 3.54" tall.

"Tetroid with 24 Heptagons, 8 colors" (February 2006) - FDM model, painted, 4" tall.

"Tetroid with 24 Heptagons, 6 colors" (January 2006) - FDM assembly, 4" tall.

"IcoVol" (October 2005) - Bronze, 6" diam.

"Hilbert_512_3D" (July 2005) -  Stainless Steel and Bronze, 5"-cube.

"Congruent Hamiltonian Cycles on the 120-Cell" (July 2005) - 3D-Print, 6" diam.

Work 2004-2005

"Borromean Torus" (June 2005) - 3D-Print, 4" diam. "DodecaHamCycle2" (June 2005) - 3D-Print, 5" diam.

"K8_19HexTangle" (June 2005) - 3D-Print, 5" diam.

"Icosahedral Volution Shell W-6T" (June 2005) - FDM, red, 3" diam.

"Icosahedral Volution Shell W-4T" (June 2005) - 3D-Print, 4" diam.

"Icosahedral Volution Shell J711-2T" (June 2005) - 3D-Print, 4" diam.

"DodecaHamCycle2" (May 2005) - FDM yellow, 3" diam.

"DodecaPentafoil Tangle" (April 2005) - Sintered Metal, 3.5" diam.

"Arabic Icosahedron" (April 2005) - 3D-Print, 5" diam.

"OctaTrefoil Cluster" (March 2005) - 3D-Print, 4" diam.

"Alter-Alterknot" (Feburary 2005) - FDM Yellow, 4" diam.

"TetraTrefoil Cluster" (Feburary 2005) - 3D-Print, 4" diam.

"TetraTrefoil Tangle" (Feburary 2005) - FDM Black, 3.5" diam.

"Triply Split Trefoil" (Feburary 2005) - FDM Yellow, 3.5" diam.

"Tangle of Two Trefoils" (Feburary 2005) - FDM red, 3.5" diam.

"Borromean Torus" (February 2005) - FDM, multiple colors, 4" diam.

"Triply Twisted Moebius Space" (February 2005) - FDM, red + black paint, 4" diam.

"Knot Divided" (January 2005) - Snow Sculpture, 12feet tall

"Hex-split Torus" (January 2005) - FDM white, 4" diam.

"Costa Surface in a Cube" (December 2004) - Bronze, 2 patinas, 5"x5"x5"

"Icosahedral Volution Shell W-4T" (November 2004) - FDM, green, 3.5" diam.

"Icosahedral Volution Shell - Scher4T" (October 2004) - FDM white, 3" diam.

"Hamiltonian Bisections of the Platonic Solids" (Octobber 2004) - FDM, multiple colors

"Double Hamiltonian Cycle" (September 2004) - 3D-Print, 8" tall

"Dodecahedral Hamiltonian Cycle" (September 2004) - FDM Black, 3" diam.

"Icosahedral Volution Shell Genus 2" (September 2004) - FDM, blue-white 3" diam.

"Dodecahedral Volution Shell Genus 2" (September 2004) - 3D-Print, 4" diam.

"Dodecahedral Volution Shell Genus 0" (September 2004) - FDM red, 2" diam.

"Totem 3" (September 2004) - Bronze, 13" tall

" Volution 's Evolution" (August 2004) - 3 bronzes, 5" cubes

Work 2003-2004

"K12 Graph on Genus-6 Surface" (June 2004) - 3D print, painted, 5"diam. "Genus-6 Kandinsky Surface" (June 2004) - 3D print, painted, 5"diam.

"Congruent Hamiltonian forming Double Volution Shell" (May 2004) - 3D-Print, 5" diam.

"3 Congruent Hamiltonian Paths on 4D Cross Polytope" (May 2004) - 3D-Print, 5" diam.

"Congruent Hamiltonian Paths on 4D Simplex" (May 2004) - 3D-Print, 3" diam.

"Congruent Hamiltonian Paths on Dodecahedral Double Shell" (May 2004) - 3D-Print, 3.5" diam.

"Sphere Eversion - Stage 5" (March 2004) - 3DcolorPrint, 6" wide {with Alex Kozlowski}

"Sphere Eversion - Stage 3" (March 2004) - 3DcolorPrint, 7" tall {with Alex Kozlowski}

"Defying Gravity" (February 2004) - FDM, white, 5"x5"x7.5"tall.

"Solar Arch" (December 2003) - Bronze, 12" diam.

"Whirled White Web" (December 2003) - Bronze, 6" tall

"Volution_5" (December 2003) - Bronze, 5" cube

"Volution_0" (December 2003) - Bronze, 5" cube

"Altamont" (December 2003) - Bronze, 4.5" diam.

"Introverted Snowball" (November 2003) - 3DPrint, 6" tall

"MorinMesh-Red/Green" (October 2003) - 3DcolorPrint, 5" tall {with Alex Kozlowski}

"MorinGrid" (September 2003) - 3DPrint, 4" tall

"Volution_5" (September 2003) - FDM white, 5" cube

"Volution_0" (August 2003) - FDM white, 5" cube

"Maloja" (August 2003) - Bronze, 4.2" diam.

"Infinit Duality" (August 2003) - another view - Bronze, 3" diam

Selected Older Pieces

"Volution_1" (June 2003) - Bronze, 5" cube "Gabo2X" (April 2003) - FDM white, 4" diam.

"Antipodal Split Trefoil Knot" (April 2003) - FDM yellow, 3" diam.

"Perspective Projection of the 600 cell" (March 2003) - 3DPrint, 8" diam. {with Mike Pao}

"Cohesion" (2002) - Bronze, 12"

"Galapagos-6" (2001) - FDM, white, 8" tall

"Bonds of Friendship" (2001) - FDM, 10" tall

"Moebius Space" (2000) - FDM black + silver paint, 4.2" diam.

"Solar Arch" (1998) - FDM white, 10" diam.

More Work, Sorted by Type

Roads on the Globe:

Max Bill Spheres:

Moebius Structures:

Scherk Collins Toroids:

Polytopes:

Math Surfaces:

Knots and Tangles:

Escher Spheres:

Large Knots, Pre_1997:

arlo Séquin

"Hilbert Cube" Stainless steel and bronze alloy, 5 inch cube, 2005

"Hilbert Cube" is a space filling recursive curve in 3 dimensions in analogy to the famous Hilbert curve in the plane.

Special care has been taken to never place more than three coplanar line segments in sequence.

At the largest recursion step the geometry has been slightly altered so as to obtain a closed loop.

"Genus-2 Costa Surface in a Cube" Bronze cast with 2-color patina. 5 inch cube, 2005

In "Genus-2 Costa Surface in a Cube" twelve quarter-arc curve segments on the faces of a cube form the three boundaries that suspend a minimal surface closely resembling the core section of a genus-2 Costa surface.

Carlo H. Séquin is a professor of Computer Science at the University of California, Berkeley. He received his Ph.D degree in experimental physics from the University of Basel, Switzerland in 1969. From 1970 till 1976 he worked at Bell Telephone Laboratories, Murray Hill, N.J., on the design and investigation of Charge-Coupled Devices for imaging and signal processing applications. In 1977 he joined the faculty in the EECS Department at Berkeley, teaching courses in integrated circuits, computer-aided design, and computer graphics. He is a Fellow of the ACM, a Fellow of the IEEE, and has been elected to the Swiss Academy of Engineering Sciences.

Séquin's work in computer graphics and in geometric design have also provided a bridge to the world of art. In collaboration with a few sculptors of abstract geometric art, in particular with Brent Collins, Séquin has found a new interest and yet another domain where the use of computer-aided tools can be explored and where new

frontiers can be opened through the use of such tools.

"Since high school I have been fascinated by geometry. I enjoyed constructing the more complicated Platonic solids with ruler and compasses, as well as reading about the 4th dimension.  While at Bell Labs in Murray Hill, I was introduced to the field of Computer Graphics in courses given by Ken Knowlton and Lilian Schwartz. In 1982, inspired by a talk by artist Frank Smullin, I started to develop the Berkeley UniGrafix rendering system, so that I could depict objects such as the "Skeleton of a Klein Bottle" or the "Granny-Knot Lattice." Since then, the focus of my work has been on computer-aided design (CAD). First I developed programs to support circuit designers, later architects and mechanical engineers. In 1995, I started a close collaboration with Brent Collins, who had been sculpting abstract geometric art for two decades. With my students, I developed a procedural "Sculpture Generator" program, to help Collins prototype potential future work in virtual form. Later programs generalized the original concepts, and eventually expanded the design space through new paradigms. In this work I see myself as a composer in the realm of pure geometry. The artistic achievement lies in finding a procedural formulation that can reflect the inherent symmetries and constructive elegance that seems to lie beneath the physical laws of our universe."

Other artwork by Carlo Séquin may be seen at: http://www.cs.berkeley.edu/~sequin/SCULPTS/sequin