       Cross reference Index to the polyhedra in StellaList 

Polyhedra are listed under the headings, some are listed several times 
since I look for them under the different classifications at different times.

Headings:

  Single stellation diagram
     Platonic solids
  Two stellation diagrams
     Archimedean solids and their duals
  Three stellation diagrams
  Four stellation diagrams

  Compounds

  By whether they have stars as faces
       ..       .....  faceted stars 

  Non-convex

  Not in 'Polyhedral Models' by M.J.Wenninger

Notes:
1. a row of ********** separate each main heading, ---------- minor ones

2. polyhedra related to others may also be listed below their 'parent' but 
indented, with a statement of how they are related, usually stellated
or truncated, but sometimes faceted.

3. The number of stellations given is the number present in the file
'StellaList' it may not be the total number thought to be possible for that
polyhedron by mathematicians.

4. The reference Wnn is the index given to that polyhedron in the book
'Polyhedron Models' by M.J.Wenninger. W00 is used for any not in that book. 
Only the first 109 models can be made by this version of !Stellate.


SINGLE STELLATION Diagram ******************************************

The Platonic Solids

W01 tetrahedron (made of 4 triangles)  --------------------------

      no stellations

       1  truncation
      W06 truncated tetrahedron 
     

W02 octahedron  (made of 8 triangles) --------------------------

    1 stellation
      W19 stella octangula

    2  faceted
     W67 Tetrahemihexahedron
     W79 Cuboctatruncated Cuboctahedron

    2  truncations
     W7 truncated octahedron
     W11 cuboctahedron - see under Archimedean solids W11

    2  hemis
      W68 Octahemioctahedron  
      W78 Cubohemioctahedron

W03 cube , hexahedron (made of 6 squares)  --------------------------

     no stellations

      1  truncation
      W8 Truncated Hexahedron

      1   quasi truncated
      W92 Stellated Truncated Hexahedron

      3  faceted
      W77 Great Cubicuboctahedron
      W85 Great Rhombicuboctahedron 
      W103 Great Rhombihexahedron

     occurs as one of the 2 stellation diagrams in

      W11 cuboctahedron = see list under Archimedean solids W11

      W103 Great Rhombihexahedron

     snub
       W17 snub cube
       
     W77 Great cubicuboctahedron
     W86 Small Rhombihexahedron

       1 hemi
     W67 Tetrahemihexahedron  

W04 icosahedron (made of 20 triangles ) --------------------------

    1  truncations
   W9 Truncated Icosahedron

   20 stellations (of the 59 known to be possible)
         the numbering is that of Wenninger
   W23 compound of  5 octahedra
   W24 compound of  5 tetrahedra
   W25 compound of 10 tetrahedra
   W26 triakis icosahedron - stellation 1
   W27 stellation 2
   W28 stellation 3
   W29 stellation 4
   W30 stellation 5
   W31 stellation 6
   W32 stellation 7
   W33 stellation 8
   W34 stellation 9
   W35 stellation 10
   W36 stellation 11
   W37 stellation 12
   W38 stellation 13
   W39 stellation 14
   W40 stellation 15
   W41 Great icosahedron
   W42 final stellation 
 
    1 truncation
      W95 truncated great icosahedron 

W05 dodecahedron (made of 12 pentagons) --------------------------

    1 truncation
    W10 Truncated dodecahedron

    3 stellations
     W20 small stellated dodecahedron 
        quasi truncated
        W97 small stellated truncated dodecahedron
     W21 Great dodecahedron 
         truncated
        W75 Truncated great dodecahedron
     W22 Great stellated dodecahedron 
       quasi truncated
       W104 Great stellated truncated dodecahedron
       truncated
       W82 Small ditrigonal dodecicosidodecahedron

    W73 Dodecadodecahedron has 12 stars on the 12 dodecahedral planes
        faceted
    W102 Great dodecahemicosahedron

****  end of Platonic Solids ****************************************

TWO Stellation diagrams  ****************************************
  
  The Archimedean solids with 2 stellation diagrams

W06 Truncated tetrahedron (made of 4 triangles, 4 hexagons) 
      dual: Triakis tetrahedron
W07 Truncated octahedron  (made of 6 squares, 8 hexagons)
      dual: Tetrakis hexahedron
W08 Truncated cube (hexahedron) (made of 8 triangles 6 octagons)
      dual: Triakis octahedron
W09 Truncated icosahedron (made of 12 pentagons 20 hexagons)
      dual: Pentakis octahedron
W10 Truncated dodecahedron (made of 20 triangles 12 decagons
      dual: Triakis icosahedron
W11 Cuboctahedron (made of 8 triangles, 2 decagons )
       dual
        W00  Rhombic dodecahedron (12 rhombi)
      2 faceted
        W68 also called an Octatetrahedron
        W78 Cubohemioctahedron

      4 stellations
        W43 Stellation 1 8 triangles 6 squares 
          compound of cube and octahedron
        W44 Stellation 2 
        W45 Stellation 3 - compound of 6 square pyramids 
        W46 Stellation 4 - final one

      3 truncations
        W15 Rhombitruncated cuboctahedron
        W79 Cuboctatruncated cuboctahedron
        W93 Great truncated cuboctahedron

       other
         W13 Rhombicuboctahedron
             faceted
           W69 Small Cubicuboctahedron

           

W12 Icosidodecahedron (made of 20 triangles, 12 pentagons
     dual
       W00  Rhombic triacontahedron
        1 stellation
         W00 Compound of 5 cubes

     similar planes but NOT a stellation
       W94 Great Icosidodecahedron

     faceted
       W89 Small Icosihemidodecahedron
       W91 Small Dodecahemidodecahedron

     stellations
      W47 Stellation  1
             compound of a dodecahedron + icosahedron
      W48 Stellation  2
      W49 Stellation  3
      W50 Stellation  4
      W51 Stellation  5
      W52 Stellation  6
      W53 Stellation  7
      W54 Stellation  8
      W55 Stellation  9
      W56 Stellation 10
      W57 Stellation 11
      W58 Stellation 12
      W59 Stellation 13
      W60 Stellation 14
      W61 Stellation 14a 
           compound of the great stellated dodecahedron
                   and the great icosahedron
      W60 Stellation 15
      W60 Stellation 16
      W60 Stellation 17
      W60 Stellation 18
      W66 Stellation 19 Last

     truncations
      W84 Icosidodecatruncated icosidodecahedron
      W16 Rhombitruncated icosidodecahedron

     other
      W81 Great ditrigonal dodecicosidodecahedron 
             also related to W88 and similar to W101
      W87 Great ditrigonal icosidodecahedron

W13 Rhombicuboctahedron
      dual trapezoidal icositetrahedron
        
W14 Rhombicosidodecahedron
      dual Trapezoidal hexecontahedron
     faceted
       W72 Small dodecicosidodecahedron
     similar version 
       W74 Small rhombidodecahedron
W15 Great rhombicuboctahedron
       dual Hexakis octahedron
W16 Great rhombicosidodecahedron
       dual Hexakis icosahedron
W17 Snub cube (laevo)
       dual Pentagonal icositetrahedron (dextro)
W18 Snub dodecahedron (laevo)
       dual Pentagonal hexecontahedron (dextro)

end Archimedean solids with 2 diagrams **************************************


Others with 2 stellation diagrams *********************************

W70 Small ditrigonal icosidodecahedron 
W78 Cubohemioctahedron  
W73 Dodecadodecahedron 
      faceted 
     W102 Great dodecahemicosahedron
W80 Ditrigonal dodecahedron 
W91 Small dodecahemidodecahedron 
W94 Great icosidodecahedron  
        similar planes to W12 the Icosidodecahedron
        related to W106 W107 
W100 Small dodecahemicosahedron
W101 Great dodecicosahedron
       similar to W81 a member of the icosidodeca family
W102 Great dodecahemicosahedron
         a faceted version of W73
W103 Great rhombihexahedron
        related to W77
W106 Great icosihemidodecahedron
        related to W94, W107
W107 Great dodecahemidodecahedron
        related to W96, W106
W109 Great rhombidodecahedron
        related to W99    

THREE Stellation diagrams ****************************************

W13 Rhombicuboctahedron
W14 Rhombicosidodecahedron
W15 Great rhombicuboctahedron
W16 Great rhombicosidodecahedron
W17 Snub cube (laevo)
W18 Snub dodecahedron (laevo)
W69 Small Cubicuboctahedron
W71 Small icosicosidodecahedron
W72 Small dodecicosidodecahedron
W76 Rhombidodecadodecahedron
W79 Cuboctatruncated cuboctahedron ( 8 squares, 6 octagons 6 8pt star )
W77 Great cubicuboctahedron ( 8 triangles (octa), 6 squares (hexa), 6 8pt *)
W81 Great ditrigonal dodecicosidodecahedron 
W82 Small ditrigonal dodecicosidodecahedron
           - a truncated form of the great stellated dodecahedron
W83 Icosidodecadodecahedron
       similar to W76
W84 Icosidodecatruncated icosidodecahedron
W85 Great rhombicuboctahedron
W88 Great icosicosidodecahedron
       related to W81
W93 Great truncated cuboctahedron
W98 Truncated dodecadodecahedron
W99 Great dodecicosidodecahedron 
W105 Great rhombicosidodecahedron 
        similar to W99
W108 Great truncated icosidodecahedron 
                30 squares 20 hexagons 12 10 pt stars
W110 Small Snub Icosicosidodecahedron
W111 Snub Dodecadodecahedron
W113 Great Inverted Snub Icosidodecahedron
W114 Inverted Snub Dodecadodecahedron
W115 Great Snub Dodeciscosidodecahedron
W116 Great Snub Icosidodecahedron
W117 Great Inverted Retrosnub Icosidodecahedron
W118 Small Inverted Retrosnub Icosicosidodecahedron
W119 Great Dirhombicosidodecahedron

FOUR Stellation diagrams ****************************************

W112 Snub icosidodecadodecahedron

  Compounds ****************************************

  Compound of :

 W19  2 tetrahedra -the stella octangula
                   the only stellation of the octahedron
 W24  5 tetrahedra - a stellation of the icosahedron
                   - has a left and right handed form
 W25 10 tetrahedra - a stellation of the icosahedron
                   - a compound of the left and right handed forms of the
                     compound of 5 tetrahedra (W24)
 W00  5 cubes      - a stellation of the rhombic triacontahedron
 W43  cube + octahedron  - 1st stellation of the Cuboctahedron
 W23  5 octahedra  - a stellation of the icosahedron
     icosahedron + dodecahedron - 1st stellation of icosidodecahedron
 W61 great icosahedron + great stellated dodecahedron
        - stellation 14a of the icosidodecahedron
 W45 6 square pyramids Cuboctahedron Stellation 3
                 
Star vertices ************************************

 W21 Great dodecahedron - a stellation of the dodecahedron
 W41 Great icosahedron  - a stellation of the icosahedron

 
5 pointed star faces ****************************************

 W70 Small ditrigonal icosidodecahedron
 W71 Small icosicosidodecahedron
 W73 Dodecadodecahedron the 12 stars are on the 12 dodecahedral planes
 W75 Truncated great dodecahedron
 W76 Rhombidodecadodecahedron
 W80 Ditrigonal dodecahedron
 W82 Small ditrigonal dodecicosidodecahedron
 W83 Icosidodecadodecahedron
 W95 Truncated great icosahedron
 W100 Small dodecahemicosahedron
 W110 Small snub icosicosidodecahedron
 W111 Snub dodecadodecahedron
 W112 Snub icosidodecadodecahedron

8 pointed star faces ****************************************

 W77 Great cubicuboctahedron
 W79 Cuboctatruncated cuboctahedron
 W93 Great truncated cuboctahedron
 W103 Great rhombihexahedron

10 pointed star faces ****************************************

 W81 Great ditrigonal dodecicosidodecahedron
 W84 Icosidodecatruncated icosidodecahedron
 W98 Truncated dodecadodecahedron
 W101 Great dodecicosahedron
        - similar to W81 but deeper holes and cups

faceted star faces ****************************************

 W85 Great rhombicuboctahedron 
         similar to W77 but faces faceted not flat stars 
 W87 Great ditrigonal icosidodecahedron
 W88 Great icosicosidodecahedron
           related to W81 Great Ditrigonal Dodecicosidodecahedron
 W90 Small dodecicosahedron
 W96 Rhombicosahedron
         closely related to W86, W83
 W102 Great dodecahemicosahedron
 W108 Great truncated icosidodecahedron 
 W109 Great rhombidodecahedron
 W113 Great Inverted Snub Icosidodecahedron
 W114 Inverted Snub Dodecadodecahedron
 W115 Great Snub Dodeciscosidodecahedron (double 5-pointed stars)
 W116 Great Snub Icosidodecahedron
 W117 Great Inverted Retrosnub Icosidodecahedron
 W118 Small Inverted Retrosnub Icosicosidodecahedron
 W119 Great Dirhombicosidodecahedron (double 5-pointed stars)

Non-convex ********************************************

 W67 Tetrahemihexahedron
 W78 Cubohemioctahedron
 W68 Octahemioctahedron
 W89 Small icosihemidodecahedron
 W86 Small rhombihexahedron
 W91 Small dodecahemidodecahedron
 
Only ones NOT Wenninger's ****************************
 
 7 labelled W00

 Deltoidal hexecontahedron (made of 60 kites ) --------------------------
        dual of the rhombicosidodecahedron

 Rhombic dodecahedron (made of 12 rhombi) --------------------------
       dual of the Cuboctahedron (an Archimedean solid)

 Rhombic triacontahedron (made of 30 rhombi ) --------------------------
       dual of the Icosidodecahedron (an Archimedean solid)

 Rhombitruncated dodecahedron (this simulates the Carbon-80 molecule)

    1 stellation
 Compound of five cubes

    2 Caged solids
 Caged dodecahedron
 Caged icosahedron
