LunchBox’s Math components enable users to create mathematically defined shapes.

#### Component Descriptions

Below, each component is described and visual examples are given. We’ve also included special Notes and Tips that can help users with less familiar situations.

#### Description

#### Appearance

#### 3D Supershapes

Creates a mathematical supershape at the origin of the Rhino document.

Learn more about supershapes *here*.

Input:

- A U Value.
*Tip:*use an even number to close the shape - A V Value
- An integer for the
*m*parameter, which determines the frequency of the deformations. - A
*b*parameter - An
*n1*parameter - An
*n2*parameter - An
*n3*parameter - An
*S*parameter, to set the scale of the object - A domain for
*D1*, which sets the number number of intervals in the horizontal direction. Tip: Set from -Pi to Pi to enclose the shape. - A domain for
*D2*, which sets the number of intervals in the vertical direction.*Tip:*Set from -Pi/2 to Pi/2 to enclose the shape.

Results:

- A supershape

#### Conoid Surface

Creates a mathematical conoid surface.

Input:

- A
*U*Value - A
*V*Value - an
*R*parameter, which affects the height of the shape - A
*T*parameter, which affects the number of revolutions of the shape. - An
*S*value, which scales the shape - A domain for
*D1* - A domain for
*D2*

Results:

- A conoid surface

#### Enneper Surface

Creates a mathematical Enneper Surface, a self-intersecting minimal surface, at the origin of the Rhino document.

Input:

- A U Value
- A V Value
- an R parameter. This affects the frequency of the variations around the edges of the shape.
- A domain for D1, which affects the overall width of the shape.
- A domain for D2, which affects the radial area of the shape.

Results:

- An Enneper surface

#### Helicoid Surface

Creates a Helicoid surface around the Rhino document’s origin point

Input:

- A U value
- A V value
- An integer for the
*R*parameter, which affects the frequency width of the spiral in the V direction - An integer for the
*T*parameter, which subdivides the frequency width set by*R* - An integer for
*S*, which sets the scale of the object - A domain for
*D1*, which affects the outer radius of the object - A domain for D2, which affects the height of the object (the number of periods)

Results:

- A helicoid surface

#### Hyperbolic Paraboloid

Creates a Hyperbolic Paraboloid

Input:

- A U value
- A V value
- A parameter for
*a*, which sets the parabola width for the paraboloid in one direction - A parameter for
*b*, which sets the parabola width for the paraboloid in one direction - An integer to set
*S*, which affects the scale of the object - A domain for
*D1*, which affects the length of the Paraboloid - A domain for
*D2*, which affects the depth of the paraboloid

Results:

- A hyperbolic paraboloid shape

#### Klein Surface

Creates a mathematical Klein surface about the origin of the document.

Input:

- A U value
- A V value
- An integer for the
*R*parameter, which affects width (radius) of the object - An integer for the
*T*parameter, which affects the incremental rotation of the cross sectional geometry of the object. - An integer to set
*S*, which affects the scale of the object - A domain for
*D1*, which affects length of the object.*Note:*0 to 4*Pi*is 2 complete rotations. - A domain for
*D2*, which affects completion of the cross sectional geometry of the object.*Note:*0 to Pi completes the rotation.

Results:

- A Klein surface

#### Mobius Surface

Creates a mathematical Mobius surface about the origin point of the document.

Input:

- A U value
- A V value
- An integer for the
*R*parameter, which affects width (radius) of the object - An integer for the
*T*parameter, which affects the incremental rotation of the cross sectional geometry of the object. - An integer to set
*S*, which affects the scale of the object - A domain for
*D1*, which affects length of the object.*Note:*-Pi to*Pi*is 1 complete rotation. - A domain for
*D2*, which affects the width of the cross sectional geometry of the object, about the midpoint of the cross-section.

Results:

- A mobius surface

#### Torus Surface

Creates a mathematical torus (the most delicious of the mathematical surface shapes) about the origin point of the document.

Input:

- A U value
- A V value
- An integer for the
*C*parameter, which affects width (radius) of the object - An integer for the
*R*parameter, which affects width (radius) of the cross-sectional geometry of the object - An integer for the
*T*parameter, which affects the length of the cross-sectional geometry of the object. - An integer to set
*S*, which affects the scale of the object - A domain for
*D1*, which affects the length of the object along its horizontal plane. - A domain for
*D2*, which affects the length of the object along its cross-sectional plane.

Results:

- A torus.

#### Platonic Cube

Creates a mathematical Platonic Cube about a specified plane.

Input:

- A list of planes, which will determine the location(s) of the results.
- An integer for the radius of a sphere. The resulting platonic form will fit inside the sphere.
- An integer between 0 and 1 to determine the amount of truncation at the corners of the cube. This adjusts also the object’s size to fit inside the radius of the theoretical sphere.

Results:

- A list of platonic cubes.

#### Platonic Dodecahedron

Creates a Platonic Dodecahedron about the given plane.

Input:

- A list of planes, which will determine the location(s) of the results.
- A integer to set the Radius of the object

Results:

- A platonic dodecahedron shape

#### Platonic Icosahedron

Creates a Platonic Icosahedron about the given plane.

Input:

- A list of planes, which will determine the location(s) of the results.
- An integer for the Radius of the shape.
- An integer between 0 and 1 to determine the amount of truncation at the corners of the shape.

Results:

- A Platonic Icosahedron

#### Platonic Octahedron

Creates a Platonic Octahedron about the given plane.

Input:

- A list of planes, which will determine the location(s) of the results.
- An integer for the Radius of the shape.
- An integer between 0 and 1 to determine the amount of truncation at the corners of the shape.

Results:

- A platonic octahedron

#### Platonic Tetrahedron

Creates a Platonic Tetrahedron about the given plane.

Input:

- A list of planes, which will determine the location(s) of the results.
- An integer for the Radius of the shape.
- An integer between 0 and 1 to determine the amount of truncation at the corners of the shape.

Results:

- A platonic tetrahedron