Legend:Value 1Value 2Value 3Value 4
Links:Adjacent swap 1-2Adjacent swap 2-3Adjacent swap 3-4

Permutohedron

This permutohedron represents all permutations of a 4-element set and is embedded in 3-dimensional space. A CliftonStrengths permutohedron, by contrast, would represent all 34-element permutations and exist in 33 dimensions. Use the 3D model and table to examine the structure of permutations, their distances, and interrelationships. The permutohedron is a geometric structure where each vertex corresponds to a unique ordering of a fixed set. In this model, each point represents a distinct permutation of four elements, positioned and colored according to weighted barycentric coordinates. Applied to CliftonStrengths, the permutohedron can represent the full ranking of an individual's 34 talent themes. By embedding these rankings into a high-dimensional permutohedron, permutation-based distances can be used to group individuals with similar profiles. This enables more detailed analysis and visualization of shared patterns within strengths-based teams or populations.
Permutations Table
Each row below represents a unique permutation of the four base values, matching a node in the 3D permutohedron visualization. The colored dot in each row uses the same color as the corresponding node in the 3D model.

ColorValue 1Value 2Value 3Value 4
1234
1243
1324
1342
1423
1432
2134
2143
2314
2341
2413
2431
3124
3142
3214
3241
3412
3421
4123
4132
4213
4231
4312
4321
Permutation Distances
Select two permutation nodes to view all distances.
Hamming
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Kendall tau
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Spearman footrule
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Cayley
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Euclidean
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Positional weighted Kendall tau
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Glossary