If you juxtapose a regular hexagon to an equilateral triangle (where all the edges of both polygons share 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 share 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 webmaster.
If you have any problems you think we might enjoy, please send them in. All replies should be sent to: email@example.com
01/31/2014 @ 01:00 PM EST
Solution: 03/03/2014 @ 01:00 PM EST
List Updated: 02/13/2014 @ 01:00 PM EST
People who answered correctly:
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)
Radu-Alexandru Todor (02/24/2014 12:56 PM EDT)
Daniel Bitin (02/26/2014 02:56 PM EDT)
David Greer (02/27/2014 12:22 PM EDT)
William Heller (02/28/2014 05:35 AM EDT)
Attention: If your name is posted here and you wish it removed please send email to the webmaster.