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Wythoffian operator

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Birectified cube sequence

Some example operations on a cube

Wythoffian operators apply to regular polytopes in dimensions up to 5.

According to Norman Johnson, the fundamental cutting operations are:

  1. Truncation - cuts vertices (truncating vertices) (polygons and higher)
  2. Cantellation - cuts edges (beveling edges) (polyhedron and higher)
  3. Runcination - cuts faces (planing faces) (polychoron and higher)
  4. Stericating - cuts cells (soliding cells) (5-polytopes and higher) (Like steradian)

See also

  Step J-abbr Johnson   Bowers
  0 - Rectified   Rectated
  1 t Truncated   Truncated
  2 c Cantellated   Rhombated
  3 r Runcinated   Prismated
  4 s Stericated   Cellated

This table shows the operator names used by Johnson and Bowers. Bowers notation is similar, but uses a great prefix to group a complete set of 2 or more lower operations together.

      Right->left          
t-notation Rings First Binary B-Ind Op-Ind J-ab Johnson name Bowers name
t_0 1 1 00001 1 1 0 regular regular
t_1 1 2 00010 2 2 1 rectified rectated
t_2 1 3 00100 4 3 2 birectified birectated
t_3 1 4 01000 8 4 3 trirectified trirectated
t_4 1 5 10000 16 5 4 quadrirectified quadrirectated
t_0,1 2 1 00011 3 7 t1 truncated truncated
t_1,2 2 2 00110 6 8 t2 bitruncated bitruncated
t_2,3 2 3 01100 12 9 t3 tritruncated tritruncated
t_3,4 2 4 11000 24 10 t4 quadritruncated quadritruncated
t_0,2 2 1 00101 5 12 c1 cantellated small rhombated
t_1,3 2 2 01010 10 13 c2 bicantellated small birhombated
t_2,4 2 3 10100 20 14 c3 tricantellated small trirhombated
t_0,3 2 1 01001 9 16 r1 runcinated small prismated
t_1,4 2 2 10010 18 17 r2 biruncinated small biprismated
t_0,4 2 1 10001 17 19 s1 stericated small cellated
t_0,1,2 3 1 000111 7 22 ct cantitruncated great rhombated
t_1,2,3 3 2 01110 14 23 ct2 bicantitruncated great birhombated
t_2,3,4 3 3 11100 28 24 ct3 tricantitruncated great trirhombated
t_0,1,3 3 1 01011 11 26 rt1 runcitruncated prismatotruncated
t_1,2,4 3 2 10110 22 27 rt2 biruncitruncated biprismatotruncated
t_0,2,3 3 1 01101 13 29 rc1 runcicantellated prismatorhombated
t_1,3,4 3 2 11010 26 30 rc2 biruncicantellated biprismatorhombated
t_0,1,4 3 1 10011 19 32 st1 steritruncated cellitruncated
t_0,2,4 3 1 010101 21 34 sc1 stericantellated small cellirhombated
t_0,3,4 3 1 11001 25 36 sr1 steriruncinated celliprismated
t_0,1,2,3 4 1 01111 15 42 rct1 runcicantitruncated great prismated
t_1,2,3,4 4 2 11110 30 43 rct2 biruncicantitruncated great biprismated
t_0,1,2,4 4 1 10111 23 45 sct1 stericantitruncated great cellirhombated
t_0,1,3,4 4 1 11011 27 47 srt1 steriruncitruncated celliprismatotruncated
t_0,2,3,4 4 1 11101 29 49 src1 steriruncicantellated celliprismatorhombated
t_0,1,2,3,4 5 1 11111 31 57 srct1 steriruncicantitruncated great cellated

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