Polyhedron With Optional Inequality Planes

This page has a CDF with a single 3D graph. If you do not see any graphs below these lines of text, you need to install the free CDF player from the Wolfram website. A few things you might want to know about it first can be found at the bottom of here.

It often crashes the first time. Try reloading. Try using a different browser if it never works (I suggest Chrome).

The 3D graph shows the polyhedron where all four inequalities are satisfied.

To see the planes for each inequality, select the "Planes" check box to the left of the graph (currently the only choice is to see all planes or no planes, but options could be added to see subsets of the full set of planes).

Graphs of the inequalities individually are available here.

The planes of the four inequalities (when shown) are color-coded based on the legend to the right.

The value of c is normalized to c = 1 - a - b - d.

The value of λ can be changed using the λ slider. Below the λ slider are sliders to control the upper bound (maxλ) and step size (stepλ) of the λ slider so that you can change what you can easily visualize by dragging the bar in the λ slider. You can always type a value into the text box below a slider to make it take a specific value. The play button below the λ slider makes it change the value of λ automatically (there are also buttons to control the speed and direction).

You can change the opacity of the shaded region using the "opac" slider. When opacity is 0, the graph shows only the planes.

You can change its size using the "size" slider.

To see grid lines over the faces of the cube (currently only on three faces), select the "Gridlines" check box.

Click and drag the graph to rotate it along any axis.

Refresh the webpage to return everything to the initial state.