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# Cross-Hatched Cube

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box.mws

The Cross-Hatched Cube

by Laurie L. Lacey, Ph.D., Schenectady County Community College, USA, laceyll@gw.sunysccc.edu, 2001 Laurie L. Lacey

NOTE: This aesthetically pleasing, albeit sinister creature, showed up while Calculus III applications of Maple were being investigated.

Introduction:

Maple can be used to stimulate the imagination. Three-dimensional objects can be plotted and viewed as one would the clouds in the sky. This flight of fancy was inspired by the exercises in in a Calculus III text [1].

> restart;

> with(plots):

```Warning, the name changecoords has been redefined
```

The Box

The reader is encouraged to try the following 3D plots as well as some of their own design.

> implicitplot3d( {x/5=z/5,x/5=-z/5,x/5=y/5,-y/5=z/5,-x/5=y/5,y/5=z/5}, x=-5..5, y=-5..5, z=-5..5, style=patchnogrid, orientation=[60,60]);

With some more exotic plot options and a spin, it can look even cooler.

> n:=20;

> for i from 1 to 30 do
angle := i*360/n;
p[i]:= implicitplot3d( {x/5=z/5,x/5=-z/5,x/5=y/5,-y/5=z/5,-x/5=y/5,y/5=z/5}, x=-5..5, y=-5..5, z=-5..5, style=patchnogrid, orientation=[angle,122]):
end do:
display(seq(p[i], i=1..n), insequence=true, lightmodel=light1);

>

>

>

[1] Larson, Hostetler, and Edwards, Multivariable Calculus , 6th edition, Houghton Mifflin Company, 1998.

Disclaimer: While every effort has been made to validate the solutions in this worksheet, Waterloo Maple Inc. and the contributors are not responsible for any errors contained and are not liable for any damages resulting from the use of this material.