Augmented Aztec bipyramid and dicube tilings

Sunmook Choi, Sangyop Lee, Seungsang Oh

Research output: Contribution to journalArticlepeer-review


We consider the enumeration of dicube tilings, where each tiling represents a three-dimensional tessellation of a polycube using dicubes. While the enumeration of domino tilings of polycubes like the Aztec diamond and the augmented Aztec diamond is well studied, we focus on the three-dimensional analogue, the augmented Aztec bipyramid. This polycube consists of unit cubes and resembles a Platonic octahedron. In this paper, we find a bijection between dicube tilings of the augmented Aztec bipyramid and three-dimensional Delannoy paths, and use this correspondence to determine the number of dicube tilings of the augmented Aztec bipyramid.

Original languageEnglish
Article number113735
JournalDiscrete Mathematics
Issue number1
Publication statusPublished - 2024 Jan

Bibliographical note

Publisher Copyright:
© 2023 Elsevier B.V.


  • Aztec bipyramid
  • Dicube tiling
  • Perfect matching

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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