Dandelion

[Dandelion]

A dense ball of 72 woven stars made from 420 paperclips.

Designed and constructed in August, 2012.

[Dandelion: inside]

The view from inside the Dandelion sculpture highlights the stars' central swirls.

[A dandelion seed head]

The stars in the Dandelion sculpture remind me of the "parachutes" in a dandelion seed head.

Image credit: Wikimedia Commons, 2009, public domain. Accessed 8/23/2012.

In this sculpture, 72 monochromatic paperclip stars (420 paperclips in all) fight for space around a closely-knit ball. The 5 or 6 clips in each star meet in a central spiral, and these are especially visible in this view from inside the ball. The sculpture's name stems from the paperclip stars' resemblance to the "parachutes" surrounding a dandelion seed head.

The star spirals are located at the vertices of a polyhedron known as the pentakis snub dodecahedron, obtained by replacing each pentagon in a snub dodecahedron with 5 triangles as shown below (left). Dually, each star spiral is located at the center of a face of a polyhedron made of 12 pentagons and 60 hexagons, also shown below (right). The latter polyhedron is an example of a buckyball, and its edges are naturally outlined in the Dandelion sculpture, with two clips per edge. The 12 white stars correspond to the 12 pentagons in this buckyball. Read more about the mathematics of buckyballs here.

The construction method used in Dandelion can be easily adapted to build other buckyball polyhedra, or more generally, other trivalent polyhedra.

[Pentakis snub dodecahedron and its dual]

Left: the pentakis snub dodecahedron is made by erecting triangles on the pentagons of a snub dodecahedron. Right: the dual polyhedron is a buckyball with 12 pentagons and 60 hexagons. Both are shown in canonical form.

Copyright © 2011–2016 by Zachary Abel. All rights reserved. Last updated on 9/29/2016.