If each side of a tetrahedron is an equilateral triangle...

Answer by Ohm0
Submitted on 6/26/2005
Rating: Not yet rated	Rate this answer:
-All white/black -Any one white/black -Two white/black, both adjacent -Two white/black, both sharing a single vertex -Two white/black, opposite of each other -Three white/black; one face shares a side with each of the other two white faces -Three white/black; two faces adjacent, and one sharing a vertex with either of them -Half-and-half; all like faces sharing a single vertex -Half-and-half; three like faces sharing a single vertex, and the fourth could be on any of the other three faces that do not share the same vertex (four combos, there!) Unless I erred, that's 17 distinct permutations. It holds to a linear pattern: 5 for a four-sider, 11 for a six-sider, 17 for an eight-sider. I'm not checking on a deca- or dodecahedron :)

FAQS.ORG makes no guarantees as to the accuracy of the posts. Each post is the personal opinion of the poster. These posts are not intended to substitute for medical, tax, legal, investment, accounting, or other professional advice. FAQS.ORG does not endorse any opinion or any product or service mentioned mentioned in these posts.

<< Back to general questions

[ Home | FAQ-Related Q&As | General Q&As | Answered Questions ]

Question by Craig Wing
Submitted on 11/4/2003
Related FAQ: N/A
Rating:	Rate this question:
If each side of a tetrahedron is an equilateral triangle painted white or black, five distinct patterns are possible: all sides white, all black, just one side white, just one black, and two sides white and two black. If each side of an octahedron is a white or black equilateral triangle, how many distinct patterns are possible?

Answer by Ronny Imir
Submitted on 9/6/2004
Rating: Not yet rated	Rate this answer:
Aline Elmann E-mail me at www.sushiman427@aol.com

Answer by Razorman
Submitted on 10/5/2004
Rating: Not yet rated	Rate this answer:
More than that.

Answer by jcm32931
Submitted on 9/12/2005
Rating: Not yet rated	Rate this answer:
27 distinct patterns. 9 different situations: 8B/0W, 7B/1W, 6B/2W, 5B/3W, 4B/4W, 3B/5W, 2B/6W, 1B/7W, 8W. Distinct patterns in that order: 1,1,3,5,7,5,3,1,1 Sum = 27. I applied Graph Theory from Discrete Math, and considered each face of the Octahedron as a Vertex of a Cube, then applied nomenclature as follows: Adjacent (shared edge), Non-Adjacent (shared face) or Opposite (nothing shared).

Answer by AuKt87
Submitted on 3/28/2006
Rating: Not yet rated	Rate this answer:
Nineteen.

Answer by barryc10
Submitted on 10/28/2006
Rating: Not yet rated	Rate this answer:
If I'm correct, there are 12 different possibilities: all white, all black, 1 side white, 1 side black, 2 white, 2 black, 3 white, 3 black, half white, half black, 5 white, 5 black.

Your name or nickname:
If you'd like to create a new account or access your existing account, put in your password here:
Your answer: