              HELP/GLOSSARY information for  
        !PolyDraw. !PolyNet, !PolySymm & !Stellate    07 Oct 2001

Names of Polyhedra

  Polyhedra were first studied by people like Plato and Archimedes, so they
have names based on ancient Greek words. The names are made up of several
parts, depending on whether they refer to 2 or 3D objects, and the number of
sides or faces.
         
  Part of 
   word    meaning                     example

   poly-    many                       a 'polygon' is a 2D figure
  -gon     a plane figure, 2D          a 'polygon' has many sides
  -hedron  a 3D solid
  -hedra   more than one 3D solid

  tetra-    4 faces                   a 'tetrahedron' is a 3D solid
  penta-    5 sides or faces                          with 4 faces
  hexa-     6 sides or faces 
  octa-     8 sides or faces        
  deca-     10 sides or faces       rhombi - a 4 sided polygon, with all 
  dodeca-   12 sides or faces           sides equal but not all angles
  icosa-    20 sides or faces       
  triaconta-30 sides or faces       delta - a triangle, or 3 sided polygon
  hexeconta-60 sides or faces          which looks like the Greek letter D

Antiprism
   a polyhedron made with two opposite faces identical regular polygons,
   with n sides, and the other faces made up of 2n equilateral triangles

Duals
 2 polyhedra are duals if the vertices of one can be put into a one-to-one 
 correspondence with the centres of the faces of the other.

Archimedean or semi-regular solids
 13 polyhedra made from more than one kind of regular polygon,
  with all vertices equal.
  5 are made by truncating the Platonic solids
  2 are 'quasi-regular' with only 2 kinds of faces, each one entirely
    surrounded by the other
  2 are made by truncating the quasi-regular ones
  2 rhombi-***
  1 snub cube
  1 snub dodecahedron 

Compound
 polyhedron made by combining 2 or more Platonic solids with the same centre
 and these solids can be seen in the polyhedron

Component
 a polyhedron which is combined with others to make a new solid, their faces 
 may be truncated or stellated so that the original polyhedron faces may ne
 changed. 

Congruent
 identically equal

Convex polygon
   one with all the angles between its edges less than 180 degrees

Convex polyhedron
   one with all its dihedral angles less than 180 degrees

Deltahedron
  has faces made only from triangles, usually equilateral

Dihedral angle
  internal angle between 2 faces which meet along a common edge

Edge of a polyhedron
  line where two faces meet

Enantiomorphic
  a polyhedron which can exist in two forms, left and right handed,
  for example, the snub cube 

Face of a polyhedron
  one of the polygons making up the surface of the polyhedron

Johnson solids
  all convex polyhedra with faces which are regular polygons, excluding
  the Platonic and Archimedean solids and the infinite sets of prisms
  and antiprisms.  

Kepler/Poinsot solids
  similar to Platonic solids but with star polygons as faces.
  compounds made from a regular polygon and its dual stuck together so that
  their edges bisect at right angles.

  They are the Stella Octangula, the great icosahedron and the 3 stellations
  of the dodecahedron

Net - see Planar Net

Planar Net - a plane shape which can be folded into a polyhedron. 
   A given polyhedron may have several different nets.
 
Platonic solids 
   The five made from convex regular polygons of the same kind, 
   with all vertices identical and all dihedral angles equal 

Polygon
   a plane figure bounded by straight edges and vertices

Polyhedron
   a set of polygons enclosing a portion of 3D space

Prism
   a polyhedron made with two opposite faces identical regular polygons, 
   with n sides and the other faces  n squares

Pyramid
   a polyhedron with a base and triangular faces all connecting the base
   to a single point above it. The base is usually a regular polygon. 

Regular polygon
  one with all sides the same length, and the internal angles between all
  the sides equal

Regular polyhedron
  As defined by Plato these are solids made from equal regular polygons.
  This is not sufficient for a truly regular solid because all the deltahedra
  (made from equilateral triangles) satisfy the condition. 
  In addition we must require all the vertices to be identical.
 
Star polygon
  one with equal length sides, but some angles at their vertices are 
   greater than 180 degrees, so they are not convex

Stellation
  a process of extending sides of polygons, (or planes of polyhedra)
  until they intersect to form another polyhedron 

Stellation diagram
  the lines formed by the projection on to one of the faces of the other 
  faces of a polyhedron

Symmetry
  if the polyhedron looks the same after you have rotated or reflected it,
  it is said to have that sort of symmetry.
  For example, rotating a cube about 90 while it is sitting on the table
  leaves it looking the same. Rotating it 4 times in the same direction gets
  it back to the original direction so it is said to be 4-fold symmetric.
  Reflecting the cube in the table also leaves it looking the same, so it is
  said to be relective (or mirror) symmetric.

Tau
  ratio of the line joining two non-adjacent vertices of a regular pentagon
  to the length of a side (also known as the Golden Section).
  Its value is (1+SQRT(5))/2

Truncated
  A polyhedron made from another by taking slices across the vertices.

Uniform polyhedron
 one with all the faces regular polygons, and all the vertices identical,
 that is, each vertex has same number of faces of the same kind arranged
 in the same order.

Vertex - point on a polyhedron where at least 3 edges meet
  
Wenninger
  A polyhedron described in the book 'Polyhedron Models' by M.J.Wenninger 
