Archimedean 1.0 Documentation Trial

Contents

Create...
Archimedean opens with "Create..." selected.  Select "Create..." to create any solid that you can define.
Predefined Solids
Polygon Palette
Polygon Buttons
Other...
New...
Create
Transform...
Select "Transform..." to transform created solids by various predefined methods.

Dual...
Antidual...
Truncate Corners...
Truncate Edges...
Resize...
New Transformation

Analyze...
Select "Analyze..." to interactively view various properties of the created solid.

Type
Name
Corners
Sides
Edges
Axes of Symmetry
Surface Area
Volume
Surface to Volume Quotient
Inscribed Radius
Circumscribed Radius

Options...
Select "Options..." to vary the method by which Archimedean displays solids.  You may also choose to create a solid with Manual Build enabled.

Fill
Draw Edges
Color Code
Draw
1st Color
2nd Color
Show Coordinates
Manual Build

Using the Video Controls
Archimedean provides a set of video controls to allow you to analytically view the assembly of a solid.
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Using the Mouse
 
 

Definitions

Create...

Platonic and Archimedean solids are distinguished by the pattern of polygonal sides around any corner.  For instance, a cube has three square faces at every corner (4 4 4) while a truncated cube has two octagons and a triangle at every corner (8 8 3).  Unless Predefined Solids is selected, you must define a corner of the solid you wish to view before Archimedean can create it.  Use the Polygon Palette to define a corner.  When you have defined the corner, click on the Create button for Archimedean to create the solid.
Predefined Solids (Default: OFF)
Select for a list by name of all Platonic and Archimedean solids as well as their duals.  Click on the name of a solid to create that solid.  While solids other than these may be created, they must be entered with the polygon palette.  For instance, a pentagonal prism would be entered by choosing a square twice and a pentagon once (4 4 5).
Polygon Palette
Select a polygon from the Polygon Palette to add another side to a corner when defining a corner in Create Mode or when adding a side to a partially built solid in Manual Mode.

Polygon Buttons

Click a polygon button to select the depicted polygon.
Other...
Choose to select a polygon unavailable through the polygon buttons.  Enter the number of sides of the desired polygon and click "OK".
New...
Select to start the creation process over.
Create
When you have chosen the sides you would like at the corner of the solid, click this to tell Archimedean to create the solid.
Transform...
Dual...
Every Platonic and Archimedean solid has a dual.  The dual is the solid created by replacing each corner of the original solid with a side whose corners are the centers of the sides that surrounded the original corner.  Another way to look at it is that the center of every side of the original solid is replaced by a corner of the dual.  The dual of a Platonic solid is another Platonic solid.  The dual of the dual of a Platonic solid is the original Platonic solid.  The dual of an Archimedean solid is neither Archimedean or Platonic and does not have a dual.

Show Dual

Reveals the dual of the current solid.
Show Original
Reveals the original solid.
Antidual...
Available only when the dual of an Archimedean solid is the current solid and New Transformation has been selected.  The antidual reverses the dual process to return the current solid to the original Archimedean solid.

Show Antidual

Reveals the antidual of the current Archimedean dual.
Show Original
Reveals the original solid.
Truncate Corners...
Uniformly slices off every corner of the solid.  Use the slider to vary the amount of truncation.  As the degree of truncation increases, Platonic solids pass through three different Archimedean solid stages before ariving at the final stage which is simply the inscribed dual.  Click on a stage name to bring the solid to that degree of truncation.
Truncate Edges...
Uniformly slices off every edge of the solid.  Use the slider to vary the amount of truncation.  Archimedean solids pass through a varying number of stages before arriving at their final stages.  Click on a stage name to bring the solid to that degree of truncation.
Resize...
Resizes the solid.
New Transformation
Select to treat a transformed solid as the starting point for further transformations.  Note that not all solids can be transformed further.
Analyze...
Type
Basic category of solid:  Platonic, Archimedean, Dual or Other.
Name
Specific name of solid.
Corners
Click to highlight the corners.  Click again to unhighlight the corners.  Click any subcategory to highlight or unhighlight that subcategory of corners.
Sides
Click to reveal all sides.  Click any subcategory to reveal only that subcategory of sides.
Edges
The number of edges.
Axes of Symmetry
Click to reveal the axes of symmetry.  Click again to hide the axes of symmetry.  Click any subcategory to reveal only that subcategory of axes of symmetry.
Surface Area
Measured in square pixels.
Volume
Measured in cubic pixels.
Surface to Volume Quotient
The sphere is the solid that has the smallest surface area of any shape for a given volume.  I have arbitrarily assigned to the sphere a surface to volume quotient of 1.  The closer a solid approaches the shape of a sphere the closer its surface to volume quotient approaches 1.
Inscribed Radius
Click to outline the largest sphere that can fit inside the current solid.  Click again to remove the outline.
Circumscribed Radius
Click to outline the smallest sphere that can fit around the current solid.  Click again to remove the outline.
Options...
Fill (Default: ON)
Make every side opaque.
Draw Edges (Default: ON)
Highlight the edges.
Color Code (Default: ON)
Every side is given a different color based on the number of edges in the side.  Available only when Fill is enabled.
Draw (Default: OFF)
Make every side transparent.
1st Color (Default: RED)
The color an original solid will be drawn in.  Use the slider to dynamically change this color.
2nd Color (Default: BLUE)
The color any new sides arising from a transformation will be drawn in.  Useful when studying the truncation process.  Use the slider to dynamically change this color.  Available only when Fill is enabled.
Show Coordinates (Default: OFF)
 
Select to display the 3D coordinates of the cursor location.  the x-axis is horizontal and increases to the right, the y-axis is the depth axis and increases as it moves away from the viewer, and the z-axis is vertical and increases as it moves up.  The 3D origin is on the screen surface at the center of Archimedean's viewing area.

Manual Build (Default: OFF)
Select to enter manual creation mode.  Creation of a solid in manual mode begins as usual in Create mode by defining the corner of the solid you wish to create and then clicking on Create.  When Manual Build is enabled Archimedean creates only one corner for you and then you must add sides one by one by selecting them from the polygon pallette and dragging them into position.  To easily position a new side into the partially built solid, drag one corner to meet the solid at the corner you would like it to join.  Archimedean will recognize the joining by highlighting the corners.  Release the mouse to complete the joining of these two corners.  Rotate the side again until another of its corners meets another corner of the partially built solid.  Release the mouse to complete the joining process.  If you would like to replace the new side before it has been completely joined, simply choose another side from the Polygon Palette.
Using the Video Controls
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Rewind the assembly process to the beginning.
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Rewind the assembly process step by step to the beginning.
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Rewind the assembly process by one step.
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Pause/Resume the assembly at the current point in the process.
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Forward the assembly process by one step.
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Forward the assembly process step by step to the end.
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Forward the assembly process to the end.
Using the Mouse
Click any where on the solid to select a surface point of the solid and then drag the mouse to rotate the solid by this surface point.  Shift-click and drag to constrain rotation to the x- or z-axis.  Click outside the surface of the solid to rotate around the y-axis.  Rotation is around the origin.  Solids are centered on the origin.  The cursor changes depending on whether the selected point is on the front or back side of the solid.  When you drag the cursor outside the bounds of the solid, Archimedean automatically considers the cursor to be on the other side.  This allows you to rotate the solid full circle by dragging the cursor back and forth in and out of the solid's bounds.
Definitions
Platonic Solid
A solid composed of regular polygonal sides of one type having a uniform pattern of sides around each corner.
Archimedean Solid
A solid composed of regular polygonal sides of two or more types having a uniform pattern of sides around each corner.
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