What question did this study set out to answer?

To determine the minimum number of vertices and k-faces in conditionally decomposable polytopes.

Lower bound results for conditionally decomposable polytopes

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Shows exact lower bounds for vertices and faces in conditionally decomposable polytopes, indicating their structural properties.

To determine the minimum number of vertices and k-faces in conditionally decomposable polytopes.
Analytical bounds for vertices and k-faces in decomposable d-polytopes
Evaluation of facets in different dimensions
Minimum vertices of a conditionally decomposable d-polytope is in the range [3d - 3, 4d - 4]
Exact lower bound of k-faces in decomposable d-polytopes with 2d + m vertices is established
In dimension 4, the minimum number of facets is 9; for d ≥ 5, it is d + 4.

Wang et al. (2026) studied this question.

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View Full Paper

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Authors

Shows exact lower bounds for vertices and faces in conditionally decomposable polytopes, indicating their structural properties.

To determine the minimum number of vertices and k-faces in conditionally decomposable polytopes.
Analytical bounds for vertices and k-faces in decomposable d-polytopes
Evaluation of facets in different dimensions
Minimum vertices of a conditionally decomposable d-polytope is in the range [3d - 3, 4d - 4]
Exact lower bound of k-faces in decomposable d-polytopes with 2d + m vertices is established
In dimension 4, the minimum number of facets is 9; for d ≥ 5, it is d + 4.

Wang et al. (2026) studied this question.

View Full Paper

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