Create Tetrahedron From a Cube in Inventor

One way to create a tetrahedron in a solid modeler is to cut it from a cube. A regular tetrahedron can be created by cutting along the diagonals of a cube as seen in the video. This instructable will first create a cube and then slice off its corners, leaving behind a regular tetrahedron. The basic steps are:

1. Create a square
2. Extrude the square into a cube
3. Slice of the corners of the cube to reveal a tetrahedron
4. Adjust the parameters of the part to specify and edge length for the tetrahedron

Click the "Origin" folder in the left-hand sidebar and then click the "XY Plane" item. Right click on it and make is visible, then create a new 2D sketch on it.

1. Select the Rectangle tool and draw a rectangle
2. Select the Dimension tool
3. Click the mouse on the top edge of the rectangle to dimension it

1. Click the equal size constraint
2. Click the top edge as one edge in the constraint
3. Click the left edge as the second edge in the constrain to set it equal to the top edge

1. Click on the parameters button
2. Click the name of the just dimensioned edge to edit
3. Name it cube_edge_length

1. Click the extrude tool button
2. Select the arrow next the extents amount
3. Click "List Parameters" in the menu
4. Select the cube_edge_length_parameter

1. Click the arrow on the Plane tool
2. Select the "Three Points" option
3. Select the three points shown to create the plane

1. Select the Split tool
2. Click on the solid icon to make the split operation give solids as a result instead of surfaces
3. Apply the tool

1. Select the just cut cube corner from the solids folder in the side bar
2. Right click on the solid and turn visibility off

Following the same steps for cutting the first face, repeat for the next three faces

1. Create a plane from three points as shown
2. Use the Split tool to cut the cube corner using the plane
3. Hide the cut corner

At this point, four cuts have been made to the cube, leaving behind a tetrahedron. To size the tetrahedron, we can set the size of the cube edge length. Once set, the change in length will propagate through the operations we've made and give the proper tetrahedron edge length.

1. Create a user parameter by clicking the "Add Numeric" button
2. Call the parameter tetra_edge_length and set it to the desired value
3. Change the existing cube_edge_length to be calculated from the tetra_edge_length parameter. Since the tetrahedron edge length is a diagonal of a cube face, the cube_edge_length is equal to sqrt(1/2)*tetra_edge_length