IBM Research | Ponder This | February 2014 challenges

# Ponder This

## February 2014

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Ponder This Challenge:

If you juxtapose a regular hexagon to an equilateral triangle (where all the edges of both polygons are of the same unit length) on a common edge - you get a polygon with five vertices; five edges; and one face.

If you juxtapose a four-dimensional pyramid whose base is a right triangular prism to a four-dimensional pyramid whose base is a tetrahedron (again: all the edges of both polychora are of the same unit length) on a common tetrahedron - how many vertices, edges, faces, and cells would the resulting polychoron have?

Update 2/12: Hint: you may use Euler's formula to check your answer.

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com

Challenge: 01/31/2014 @ 01:00 PM EST
Solution: 03/03/2014 @ 01:00 PM EST
List Updated: 02/13/2014 @ 01:00 PM EST

Dan Dima (02/01/2014 09:27 AM EDT)
Oleg Vlasii (02/02/2014 05:46 AM EDT)
Igor Novak (02/03/2014 01:54 PM EDT)
Liubing Yu (02/04/2014 03:24 AM EDT)
Florian Fischer (02/07/2014 09:37 AM EDT)
Kevin Bauer (02/09/2014 08:09 PM EDT)
Christian Blatter (02/11/2014 03:54 AM EDT)
Misha Lavrov (02/11/2014 03:52 PM EDT)
Olivier Mercier (02/12/2014 03:47 PM EDT)
Don Dodson (02/12/2014 03:54 PM EDT)
Chuck Carroll (02/12/2014 04:15 PM EDT)
Gilles-Philippe Paillé (02/12/2014 05:11 PM EDT)
Alexandre Gilotte (02/12/2014 07:29 PM EDT)
Antoine Comeau (02/12/2014 09:32 PM EDT)
Andrea Andenna (02/13/2014 12:45 AM EDT)
Todd Will (02/14/2014 11:05 PM EDT)
Cynthia Beauchemin (02/15/2014 02:13 AM EDT)
Motty Porat (02/15/2014 07:06 PM EDT)
Masoud Alipour (02/15/2014 07:21 PM EDT)
Michael Wilms (02/16/2014 06:15 AM EDT)
Mathias Schenker (02/17/2014 05:31 PM EDT)
Adam Daire (02/18/2014 12:09 PM EDT)
Armin Krauss (02/19/2014 10:31 AM EDT)
Philipp Seemann (02/19/2014 05:51 PM EDT)