A Polyhedral Journey, Beginning with the Snub Cube / Pentagonal Isositetrahedron Base/Dual Compound

The snub cube and its dual make an attractive compound. Since the snub cube is chiral, its chirality is preserved in this compound.

Penta Icositetra & snub cube compound

If you examine the convex hull of this compound, you will find it to be chiral as well.

Convex hull of snub cube& dual compound

Here is the mirror image of that convex hull:

Convex hull mirror image

These two convex hulls, of course, have twin, chiral, duals:

dual of Convex hull of snub cube& dual compound

Dual of Convex hull mirror image

The two chiral convex hulls above (the red, blue, and yellow ones), made an interesting compound, as well.

Compound of enantiomorphic pair not dual

This is also true of their chiral duals:

Compound of enantiomorphic pair

I next stellated this last figure numerous times (I stopped counting at ~200), to obtain this polyhedron:

Stellated Compound of enantiomorphic pair dual

After seeing this, I wanted to know what its dual would look like — and it was a nice polyhedron on which to end this particular polyhedral journey.

dual of Stellated Compound of enantiomorphic pair dual

I  make these transformations of polyhedra, and create these virtual models, using a program called Stella 4d. It may be purchased, or tried for free, at http://www.software3d.com/Stella.php.

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things. The majority of these things are geometrical. Welcome to my little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with the views of my employer, nor any other organization, nor institution, of any kind.
This entry was posted in Mathematics and tagged , , , , , , , , , , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s