# Part Description and Specifications for "New Toroids"

These parts will serve as a geometrical model in classes on modeling and math of minimal surfaces, and as a small scale model for artists, e.g., Brent Collins, who is doing similar sculptures in wood.

This is part of a research program sponsored by NSF to streamline the process of rapid prototyping of free form parts, by defining a clean separation and interface between designers and fabricators.

All these parts were generated with Carlo Séquin's sculpture generator

## New Monkey Trefoil

This is a new version of the 3-fold symmetrical version of a 3-storey monkey-saddle Scherk tower bent into a toroid.

Front: Side:

FILE ==> montref.stl.gz

• branches = 3
• storeys = 3
• height = 1.75
• flange = 1.50
• twist = 180.00
• azimuth = 30.00
• thickness = 0.03
• rim_bulge = 0.00
• detail = 16 {--> 39,168 triangles}

## Monkey Cinquefoil

This is a 5-storey monkey-saddle Scherk tower bent into a toroid.

Front: Side:

FILE ==> cinquefoil.stl.gz

• branches = 3
• storeys = 5
• height = 1.35
• flange = 1.40
• twist = 60.00
• azimuth = 0.00
• thickness = 0.04
• rim_bulge = 0.00
• detail = 14

## Woven Quad

This is a really nifty new structure: It is a double toroidal loop in which the first and second passage are intertwinde with one another - without intersections ! It is formed from a 9-storey Scherk tower with 4th order saddles.

Stereo:

FILE ==> wovenquad.stl.gz

• branches = 4
• storeys = 9
• height = 1.10
• flange = 0.80
• WARP = 720 degrees !
• twist = 45.00
• azimuth = 0.00
• thickness = 0.05
• rim_bulge = 0.00
• detail = 10 {--> 63,369 triangles}

### Fabrication Hints

The scale or strength of this model is not critical; it can be scaled so as to fit optimally a particular process or some remaining space in a run of a larger piece. Ideally we would like a part scaled to be 3-5 inches in diameter.

Orientation is not critical either. However, for a layered manufacturing process (SLA, SLS, etc), it might be best to turn the object 90 degrees around the x-axis, thereby giving the part minimal height, and preserving its radial symmetry ideally.

The more complicated parts, in particular the "Woven Quad" should probably be built with SLS or with some other technology where the support structure can be easily removed.

In these .STL files have not been merged (yet); so they need software that does not get upset when shared vertices appear separated by one unit in the last digit due to rounding errors.

### Part Description Files:

Compressed ASCII .STL file: FILE.stl.gz

The compressed file can be downloaded from our anonymous FTP site with:
ftp ftp.cs.berkeley.edu {login as "anonymous"; use your full e-mail address as password.}
Then change directory: cd ucb/projects/unigrafix/STL
Fetch desired files: get FILE.stl.gz
The FILE.stl.gz file can be uncompressed with gunzip.

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Page Editor: Carlo H. Séquin