# Hexicated 7-simplexes

 Orthogonal projections in A7 Coxeter plane 7-simplex Hexicated 7-simplex Hexitruncated 7-simplex Hexicantellated 7-simplex Hexiruncinated 7-simplex Hexicantitruncated 7-simplex Hexiruncitruncated 7-simplex Hexiruncicantellated 7-simplex Hexisteritruncated 7-simplex Hexistericantellated 7-simplex Hexipentitruncated 7-simplex Hexiruncicantitruncated 7-simplex Hexistericantitruncated 7-simplex Hexisteriruncitruncated 7-simplex Hexisteriruncicantellated 7-simplex Hexipenticantitruncated 7-simplex Hexipentiruncitruncated 7-simplex Hexisteriruncicantitruncated 7-simplex Hexipentiruncicantitruncated 7-simplex Hexipentistericantitruncated 7-simplex Hexipentisteriruncicantitruncated 7-simplex (Omnitruncated 7-simplex)

In seven-dimensional geometry, a hexicated 7-simplex is a convex uniform 7-polytope, including 6th-order truncations (hexication) from the regular 7-simplex.

There are 20 unique hexications for the 7-simplex, including all permutations of truncations, cantellations, runcinations, sterications, and pentellations.

The simple hexicated 7-simplex is also called an expanded 7-simplex, with only the first and last nodes ringed, is constructed by an expansion operation applied to the regular 7-simplex. The highest form, the hexipentisteriruncicantitruncated 7-simplex is more simply called a omnitruncated 7-simplex with all of the nodes ringed.

## Hexicated 7-simplex

Hexicated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,6{36}
Coxeter-Dynkin diagrams
6-faces 254:
8+8 {35}
28+28 {}x{34}
56+56 {3}x{3,3,3}
70 {3,3}x{3,3}
5-faces
4-faces
Cells
Faces
Edges 336
Vertices 56
Vertex figure 5-simplex antiprism
Coxeter group A7×2, [[36]], order 80640
Properties convex

In seven-dimensional geometry, a hexicated 7-simplex is a convex uniform 7-polytope, a hexication (6th order truncation) of the regular 7-simplex, or alternately can be seen as an expansion operation.

The vertices of the A7 2D orthogonal projection are seen in the Ammann–Beenker tiling.

### Root vectors

Its 56 vertices represent the root vectors of the simple Lie group A7.

### Alternate names

• Expanded 7-simplex
• Small petated hexadecaexon (acronym: suph) (Jonathan Bowers)[1]

### Coordinates

The vertices of the hexicated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,1,1,1,1,2). This construction is based on facets of the hexicated 8-orthoplex, .

A second construction in 8-space, from the center of a rectified 8-orthoplex is given by coordinate permutations of:

(1,-1,0,0,0,0,0,0)

### Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [[7]] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [[5]] [4] [[3]]

## Hexitruncated 7-simplex

hexitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,6{36}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges 1848
Vertices 336
Vertex figure
Coxeter group A7, [36], order 40320
Properties convex

### Alternate names

• Petitruncated octaexon (acronym: puto) (Jonathan Bowers)[2]

### Coordinates

The vertices of the hexitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,1,1,1,2,3). This construction is based on facets of the hexitruncated 8-orthoplex, .

### Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

## Hexicantellated 7-simplex

Hexicantellated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,2,6{36}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges 5880
Vertices 840
Vertex figure
Coxeter group A7, [36], order 40320
Properties convex

### Alternate names

• Petirhombated octaexon (acronym: puro) (Jonathan Bowers)[3]

### Coordinates

The vertices of the hexicantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,1,1,2,2,3). This construction is based on facets of the hexicantellated 8-orthoplex, .

### Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

## Hexiruncinated 7-simplex

Hexiruncinated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,3,6{36}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges 8400
Vertices 1120
Vertex figure
Coxeter group A7, [[36]], order 80640
Properties convex

### Alternate names

• Petiprismated hexadecaexon (acronym: puph) (Jonathan Bowers)[4]

### Coordinates

The vertices of the hexiruncinated 7-simplex can be most simply positioned in 8-space as permutations of (0,0,1,1,2,2,2,3). This construction is based on facets of the hexiruncinated 8-orthoplex, .

### Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [[7]] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [[5]] [4] [[3]]

## Hexicantitruncated 7-simplex

Hexicantitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,6{36}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges 8400
Vertices 1680
Vertex figure
Coxeter group A7, [36], order 40320
Properties convex

### Alternate names

• Petigreatorhombated octaexon (acronym: pugro) (Jonathan Bowers)[5]

### Coordinates

The vertices of the hexicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,1,1,2,3,4). This construction is based on facets of the hexicantitruncated 8-orthoplex, .

### Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

## Hexiruncitruncated 7-simplex

Hexiruncitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,3,6{36}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges 20160
Vertices 3360
Vertex figure
Coxeter group A7, [36], order 40320
Properties convex

### Alternate names

• Petiprismatotruncated octaexon (acronym: pupato) (Jonathan Bowers)[6]

### Coordinates

The vertices of the hexiruncitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,1,2,2,3,4). This construction is based on facets of the hexiruncitruncated 8-orthoplex, .

### Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

## Hexiruncicantellated 7-simplex

Hexiruncicantellated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,2,3,6{36}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges 16800
Vertices 3360
Vertex figure
Coxeter group A7, [36], order 40320
Properties convex

In seven-dimensional geometry, a hexiruncicantellated 7-simplex is a uniform 7-polytope.

### Alternate names

• Petiprismatorhombated octaexon (acronym: pupro) (Jonathan Bowers)[7]

### Coordinates

The vertices of the hexiruncicantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,1,2,3,3,4). This construction is based on facets of the hexiruncicantellated 8-orthoplex, .

### Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

## Hexisteritruncated 7-simplex

hexisteritruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,4,6{36}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges 20160
Vertices 3360
Vertex figure
Coxeter group A7, [36], order 40320
Properties convex

### Alternate names

• Peticellitruncated octaexon (acronym: pucto) (Jonathan Bowers)[8]

### Coordinates

The vertices of the hexisteritruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,2,2,2,3,4). This construction is based on facets of the hexisteritruncated 8-orthoplex, .

### Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

## Hexistericantellated 7-simplex

hexistericantellated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,2,4,6{36}
Coxeter-Dynkin diagrams
6-faces t0,2,4{3,3,3,3,3}

{}xt0,2,4{3,3,3,3}
{3}xt0,2{3,3,3}
t0,2{3,3}xt0,2{3,3}

5-faces
4-faces
Cells
Faces
Edges 30240
Vertices 5040
Vertex figure
Coxeter group A7, [[36]], order 80640
Properties convex

### Alternate names

• Peticellirhombihexadecaexon (acronym: pucroh) (Jonathan Bowers)[9]

### Coordinates

The vertices of the hexistericantellated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,2,2,3,3,4). This construction is based on facets of the hexistericantellated 8-orthoplex, .

### Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [[7]] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [[5]] [4] [[3]]

## Hexipentitruncated 7-simplex

Hexipentitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,5,6{36}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges 8400
Vertices 1680
Vertex figure
Coxeter group A7, [[36]], order 80640
Properties convex

### Alternate names

• Petiteritruncated hexadecaexon (acronym: putath) (Jonathan Bowers)[10]

### Coordinates

The vertices of the hexipentitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,2,2,2,2,3,4). This construction is based on facets of the hexipentitruncated 8-orthoplex, .

### Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [[7]] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [[5]] [4] [[3]]

## Hexiruncicantitruncated 7-simplex

Hexiruncicantitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,3,6{36}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges 30240
Vertices 6720
Vertex figure
Coxeter group A7, [36], order 40320
Properties convex

### Alternate names

• Petigreatoprismated octaexon (acronym: pugopo) (Jonathan Bowers)[11]

### Coordinates

The vertices of the hexiruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,2,2,3,4,5). This construction is based on facets of the hexiruncicantitruncated 8-orthoplex, .

### Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [[7]] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [[5]] [4] [[3]]

## Hexistericantitruncated 7-simplex

Hexistericantitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,4,6{36}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges 50400
Vertices 10080
Vertex figure
Coxeter group A7, [36], order 40320
Properties convex

### Alternate names

• Peticelligreatorhombated octaexon (acronym: pucagro) (Jonathan Bowers)[12]

### Coordinates

The vertices of the hexistericantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,2,2,3,4,5). This construction is based on facets of the hexistericantitruncated 8-orthoplex, .

### Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [[7]] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [[5]] [4] [[3]]

## Hexisteriruncitruncated 7-simplex

Hexisteriruncitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,3,4,6{36}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges 45360
Vertices 10080
Vertex figure
Coxeter group A7, [36], order 40320
Properties convex

### Alternate names

• Peticelliprismatotruncated octaexon (acronym: pucpato) (Jonathan Bowers)[13]

### Coordinates

The vertices of the hexisteriruncitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,2,3,3,4,5). This construction is based on facets of the hexisteriruncitruncated 8-orthoplex, .

### Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

## Hexisteriruncicantellated 7-simplex

Hexisteriruncitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,2,3,4,6{36}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges 45360
Vertices 10080
Vertex figure
Coxeter group A7, [[36]], order 80640
Properties convex

### Alternate names

• Peticelliprismatorhombihexadecaexon (acronym: pucproh) (Jonathan Bowers)[14]

### Coordinates

The vertices of the hexisteriruncitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,2,3,4,4,5). This construction is based on facets of the hexisteriruncitruncated 8-orthoplex, .

### Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [[7]] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [[5]] [4] [[3]]

## Hexipenticantitruncated 7-simplex

hexipenticantitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,5,6{36}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges 30240
Vertices 6720
Vertex figure
Coxeter group A7, [36], order 40320
Properties convex

### Alternate names

• Petiterigreatorhombated octaexon (acronym: putagro) (Jonathan Bowers)[15]

### Coordinates

The vertices of the hexipenticantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,2,2,2,3,4,5). This construction is based on facets of the hexipenticantitruncated 8-orthoplex, .

### Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [7] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [5] [4] [3]

## Hexipentiruncitruncated 7-simplex

Hexisteriruncicantitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,3,5,6{36}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges 80640
Vertices 20160
Vertex figure
Coxeter group A7, [36], order 40320
Properties convex

### Alternate names

• Petiteriprismatotruncated hexadecaexon (acronym: putpath) (Jonathan Bowers)[16]

### Coordinates

The vertices of the hexisteriruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,2,3,4,5,6). This construction is based on facets of the hexisteriruncicantitruncated 8-orthoplex, .

### Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [[7]] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [[5]] [4] [[3]]

## Hexisteriruncicantitruncated 7-simplex

Hexisteriruncicantitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,3,4,6{36}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges 80640
Vertices 20160
Vertex figure
Coxeter group A7, [36], order 40320
Properties convex

### Alternate names

• Petigreatocellated octaexon (acronym: pugaco) (Jonathan Bowers)[17]

### Coordinates

The vertices of the hexisteriruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,1,2,3,4,5,6). This construction is based on facets of the hexisteriruncicantitruncated 8-orthoplex, .

### Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [[7]] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [[5]] [4] [[3]]

## Hexipentiruncicantitruncated 7-simplex

Hexipentiruncicantitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,3,5,6{36}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges 80640
Vertices 20160
Vertex figure
Coxeter group A7, [36], order 40320
Properties convex

### Alternate names

• Petiterigreatoprismated octaexon (acronym: putgapo) (Jonathan Bowers)[18]

### Coordinates

The vertices of the hexipentiruncicantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,2,2,3,4,5,6). This construction is based on facets of the hexipentiruncicantitruncated 8-orthoplex, .

### Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [[7]] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [[5]] [4] [[3]]

## Hexipentistericantitruncated 7-simplex

Hexipentistericantitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,4,5,6{36}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges 80640
Vertices 20160
Vertex figure
Coxeter group A7, [[36]], order 80640
Properties convex

### Alternate names

• Petitericelligreatorhombihexadecaexon (acronym: putcagroh) (Jonathan Bowers)[19]

### Coordinates

The vertices of the hexipentistericantitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,2,3,3,4,5,6). This construction is based on facets of the hexipentistericantitruncated 8-orthoplex, .

### Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [[7]] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [[5]] [4] [[3]]

## Omnitruncated 7-simplex

Omnitruncated 7-simplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,3,4,5,6{36}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges 141120
Vertices 40320
Vertex figure Irr. 6-simplex
Coxeter group A7, [[36]], order 80640
Properties convex

The omnitruncated 7-simplex is composed of 40320 (8 factorial) vertices and is the largest uniform 7-polytope in the A7 symmetry of the regular 7-simplex. It can also be called the hexipentisteriruncicantitruncated 7-simplex which is the long name for the omnitruncation for 7 dimensions, with all reflective mirrors active.

### Permutohedron and related tessellation

The omnitruncated 7-simplex is the permutohedron of order 8. The omnitruncated 7-simplex is a zonotope, the Minkowski sum of eight line segments parallel to the eight lines through the origin and the eight vertices of the 7-simplex.

Like all uniform omnitruncated n-simplices, the omnitruncated 7-simplex can tessellate space by itself, in this case 7-dimensional space with three facets around each ridge. It has Coxeter-Dynkin diagram of .

### Alternate names

• Great petated hexadecaexon (Acronym: guph) (Jonathan Bowers)[20]

### Coordinates

The vertices of the omnitruncated 7-simplex can be most simply positioned in 8-space as permutations of (0,1,2,3,4,5,6,7). This construction is based on facets of the hexipentisteriruncicantitruncated 8-orthoplex, t0,1,2,3,4,5,6{36,4}, .

### Images

orthographic projections
Ak Coxeter plane A7 A6 A5
Graph
Dihedral symmetry [8] [[7]] [6]
Ak Coxeter plane A4 A3 A2
Graph
Dihedral symmetry [[5]] [4] [[3]]

## Related polytopes

These polytope are a part of 71 uniform 7-polytopes with A7 symmetry.

## Notes

1. ^ Klitizing, (x3o3o3o3o3o3x - suph)
2. ^ Klitizing, (x3x3o3o3o3o3x- puto)
3. ^ Klitizing, (x3o3x3o3o3o3x - puro)
4. ^ Klitizing, (x3o3o3x3o3o3x - puph)
5. ^ Klitizing, (x3o3o3o3x3o3x - pugro)
6. ^ Klitizing, (x3x3x3o3o3o3x - pupato)
7. ^ Klitizing, (x3o3x3x3o3o3x - pupro)
8. ^ Klitizing, (x3x3o3o3x3o3x - pucto)
9. ^ Klitizing, (x3o3x3o3x3o3x - pucroh)
10. ^ Klitizing, (x3x3o3o3o3x3x - putath)
11. ^ Klitizing, (x3x3x3x3o3o3x - pugopo)
12. ^ Klitizing, (x3x3x3o3x3o3x - pucagro)
13. ^ Klitizing, (x3x3o3x3x3o3x - pucpato)
14. ^ Klitizing, (x3o3x3x3x3o3x - pucproh)
15. ^ Klitizing, (x3x3x3o3o3x3x - putagro)
16. ^ Klitizing, (x3x3x3x3o3x3x - putpath)
17. ^ Klitizing, (x3x3x3x3x3o3x - pugaco)
18. ^ Klitzing, (x3x3x3x3o3x3x - putgapo)
19. ^ Klitizing, (x3x3x3o3x3x3x - putcagroh)
20. ^ Klitizing, (x3x3x3x3x3x3x - guph)

## References

• H.S.M. Coxeter:
• H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
• Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6, wiley.com
• (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
• (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
• (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
• Norman Johnson Uniform Polytopes, Manuscript (1991)
• N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, PhD (1966)
• Klitzing, Richard. "7D". x3o3o3o3o3o3x - suph, x3x3o3o3o3o3x- puto, x3o3x3o3o3o3x - puro, x3o3o3x3o3o3x - puph, x3o3o3o3x3o3x - pugro, x3x3x3o3o3o3x - pupato, x3o3x3x3o3o3x - pupro, x3x3o3o3x3o3x - pucto, x3o3x3o3x3o3x - pucroh, x3x3o3o3o3x3x - putath, x3x3x3x3o3o3x - pugopo, x3x3x3o3x3o3x - pucagro, x3x3o3x3x3o3x - pucpato, x3o3x3x3x3o3x - pucproh, x3x3x3o3o3x3x - putagro, x3x3x3x3o3x3x - putpath, x3x3x3x3x3o3x - pugaco, x3x3x3x3o3x3x - putgapo, x3x3x3o3x3x3x - putcagroh, x3x3x3x3x3x3x - guph