Polyhedra Programming Contest

Introduction

You are asked to describe 25 different polyhedra. To describe a polyhedron, you give the coordinates of its vertices in space and specify which vertices are connected by edges.

The objective is to find polyhedra that have the largest possible surface area while adhering to certain design constraints.

For example:

• For n = 4, the tetrahedron with vertices at (1, 2, 2), (2, 1, 1), (3, 3, 4) and (4, 4, 3) satisfies the design constraints. Its surface area is 11.57976.
• For n = 4, the tetrahedron with vertices at (2, 3, 1), (3, 2, 1), (1, 1, 4) and (4, 4, 3) does not satisfy the design constraints since there are two vertices for which the z-coordinate equals 1.
• For n = 4, the tetrahedron with vertices at (1, 2, 1), (2, 4, 2), (3, 1, 3) and (4, 3, 4) does not satisfy the last design constraint since the four vertices all lie in the same plane. It isn't a solid, it's flat, and no amount of reshaping can turn a 2-dimensional object into a sphere.

Email me your best polyhedron for each value of n from 4 to 28. I’ll calculate a subscore for each polyhedron (details of the scoring system are below) and the total of your 25 subscores will be your contest score. The person with the highest contest score wins five hundred US dollars ($500). Second place wins $100. Third prize is the software package Cabri Geometry II Plus, donated by Cabrilog.

How to Enter

Send an email containing your entry to bitzenbeitz@aol.com. Put just the word POLYHEDRA in the subject line.

The body of the email should consist of:

• the descriptions of your polyhedra, followed by
• a hash sign (#) to indicate that there are no more polyhedra, followed by
• a single line with your name, and then finally
• a single line with your location (city, state, country).

There can be any number of polyhedra in a single entry. For example, here’s the body of an email with two polyhedra:

Let’s have a closer look at the way an individual polyhedron is described. There’s one face on each line. Each face, except the last, ends with a semicolon. The last face ends with a period. Each face has three vertices (separated by commas), and each vertex has three coordinates (enclosed in parentheses and separated by commas).

You can insert spaces and blank lines freely to improve readability of the entry.

Do not include any extraneous information anywhere in the entry. Entries are processed by computer and you know how finicky they can be.

You may enter as often as you like.

Entries must be received by June 22^nd at Noon in Geneva, Switzerland. Geneva’s time zone is GMT +01:00. Be aware that Geneva switched from standard time to daylight saving time on March 30^th. If you are not sure what time it is in Geneva right now, please visit this site or this one.

The Scoring System

Each time you submit an entry I will merge it with your prior entries. The result will be a virtual entry containing your best polyhedron for each of the 25 values of n. I will give each of these 25 polyhedra a subscore from 0 to 1 and their sum will be your contest score.

I score the individual polyhedra as follows. If your polyhedron is the best that was submitted for that n, I give it 1 point; otherwise I give it only a fraction of a point. The fraction is its surface area divided by the largest surface area submitted for that n. For example, suppose your polyhedron with 4 vertices has a surface area of 12 and further suppose that the largest 4-vertex surface area that was submitted to the contest was 15. Then your subscore for n = 4 is 12 / 15 = 0.800.

Getting Your Questions Answered

First, check the FAQ section below. If you can't find the information you need there, send your question to the discussion list. If your question is of a personal nature, you can send email directly to alzimmerma@aol.com.

The Discussion List

If you think you might enter the contest, it is important that you join the contest discussion list by clicking here. The discussion list serves two purposes. First, it allows people to ask for clarifications to the rules. Be aware that sometimes these requests result in changes to the rules, and the only place those changes are announced is on the list. Second, the list allows contestants to interact with each other to discuss programming techniques, results and anything else relevant to the contest.

Acknowledgment

This contest is based on an extension to a problem by Cihan Altay.

My Lawyer Would Want Me To Say This

I reserve the right to discontinue the contest at any time. I reserve the right to disqualify any entry or entrant for any reason that suits me. I reserve the right to interpret the rules as I see fit. I reserve the right to change the contest rules in mid-contest. In all matters contest-related, my word is law.

Frequently Asked Questions

Do I have to submit a polyhedron for every n from 4 to 28?

No. You’ll receive a subscore of 0 for any n that you’ve submitted no polyhedron for.

How will I know that you’ve received my entry?

When I receive an entry I process it with the automated Parser/Scorer and then send a confirmation back to the submitter. Although the Parser/Scorer is automated, the process of getting entries into the Parser/Scorer is not, so it may take as long as 24 hours for you to receive your confirmation.

Are teams eligible to enter?

Teams are discouraged, but not forbidden. If you want to form a team, email me and we'll discuss it.

Polyhedra Contest Standings — Al Zimmermann's Programming Contests

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