Quintessence Schleimer and Segerman

The goal of this family of burr puzzles, collectivelycalled Quintessence, is to assemble collections of ribs intoself-supporting structures. The ribs are shown immediatelyto the right.

The ribs are divided into three sets: Meteor, Pulsar, andInflation. These are shown below-right, in order and arealso described in the table at the bottom of this page. Thesets may be purchased from Shapeways.

http://shpws.me/nv5G

http://shpws.me/nv5Q

http://shpws.me/nv5F

Each rib is made from four, five, or six dodecahedral cells(D) in the cell-centered projection (c) of the spherical120–cell to three-space. A puzzle receives the designationDcN where N counts the number of cells. Twelve of themany possible burr puzzles are pictured on the followingpages.

In every case, assembling the puzzle relies on the ribs beingslightly flexible. For some puzzles a very small amount ofpressure may be needed to place the final rib. The ribs canbe washed in hot water to clean them; this will also resetthe shapes of ribs that have become loose. We now list thesets and the ribs they contain. Note that the two equatorsare mirror images, and are not interchangeable.

spineinner six outer six

inner four outer four equator

Set\rib name inner four outer four inner six outer six spine equator a equator bMeteor 6 6 0 0 1 0 0Pulsar 0 0 0 6 0 0 0Inflation 0 0 6 0 1 1 1

On the following pages we show several of the many possible puzzles. Please share withus any new ones that you find!

Quintessence Schleimer and Segerman

Dc24 Star6× inner fourUp to three ribs

can be replaced

by inner sixs.

Dc24 Pulsar6× inner fourAny number of ribs

can be replaced by

inner sixs.

Dc29 Space Invader2× inner six2× outer six1× spineCan add 2× equator.

Dc30 Star3× outer four3× outer six

Dc30 Ring5× outer sixReplace all ribs with

inner sixs to get the

Inner Ring.

Dc30 Comet5× outer sixAdd a spine and one

inner four to make the

Comet more rigid.

Quintessence Schleimer and Segerman

Dc36 Alien3× inner six3× outer sixEither set of 6s can

be replaced by 4s.

Dc36 Pulsar6× outer sixUp to three ribs

can be replaced

by outer fours.

Dc42 Alien6× outer four3× inner six

Dc45 Meteor5× inner four5× outer four1× spineThere are six ways

to build this.

Dc50 Galaxy5× inner four5× outer four2× equator

Dc75 Meteor5× inner six5× outer six1× spine2× equator