Determining Polyhedron Name from Given Description

Date: 11/16/2003 at 22:48:25
From: Howard
Subject: Name of the geometric solid specified below

What is the name of the geometric solid having 7 faces, 10 vertices, 
and 15 edges?  Thank you!

Date: 11/17/2003 at 09:54:27
From: Doctor Peterson
Subject: Re: Name of the geometric solid specified below

Hi, Howard.

A question like this will not have a single answer; most polyhedra 
have no special name, and most of those that do are defined by 
special features such as parallel edges or congruent faces, so they 
would not apply to the kind of general situation you are asking 
about.  For example, if a prism has this number of faces, edges, and 
vertices, and you stretch the bottom, you can change it first to a 
frustum of a pyramid, and then to a nameless distorted prism, without 
changing the fact that it fits your description!

But you can look for _a_ familiar polyhedron that fits, rather than a 
name that applies to _every_ such polyhedron.  To do that, you can 
start by looking for properties of familiar polyhedra in terms of 
their faces, vertices, and edges.  For example, suppose you have a 
prism whose base is an n-gon.  There are n lateral faces and 2 top and 
bottom faces; n vertices each on the top and bottom; and n edges each 
on the top, bottom, and sides.  So you have

  F = n + 2
  V = 2n
  E = 3n

Do the same for several other kinds of shapes (pyramids, perhaps 
regular polyhedra and some others), and see whether what you are given 
fits any of those.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 11/17/2003 at 12:37:06
From: Howard
Subject: Thank you (Name of the geometric solid specified below)

Thank you so very, very much for your prompt response to my question. 
I appreciate your efforts.

Howard