A Variant of the Rhombic Enneacontahedron

A Variation On the Rhombic Enneacontahedron

In the rhombic enneacontahedron, which is shown below, there are thirty narrow rhombi (shown in red) which separate twelve panels of five rhombi each (shown in yellow). This polyhedron is familiar to many people:

Zonohedrified Dodeca

As you can see, the rhombic enneacontahedron has three of these yellow panels meeting at some of its vertices, along with three of the red, narrow rhombi.

For this new variant, at the top of this post, the five-rhombi panels are rotated until only two of them (rather than three) meet at certain vertices, and the thirty red, narrow rhombi between the yellow five-rhombi panels are replaced by twenty equilateral (but non-equiangular) hexagons, also shown in red.

Both of these polyhedra are related to the Platonic dodecahedron, which is shown below. In the rhombic enneacontahedron, the red, narrow rhombi correspond in position to the thirty edges of a dodecahedron. In the new variant, the red hexagons correspond to the vertices of a dodecahedron, rather than its edges. In both of these red-and-yellow polyhedra, the yellow, five-rhombi panels correspond to the dodecahedron’s faces. To see this more clearly, just compare the polyhedra above with this dodecahedron:

Dodecahedron

(All polyhedral images here were created with Stella 4d: Polyhedron Navigator, which you can try and/or buy here.)

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.
Image | 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