Truncated triangular pyramid number
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Truncated Triangular Pyramid Number[1] are achieved by removing (truncating) some smaller Tetrahedral number (or triangular pyramidal number) from each of the vertices of a bigger Tetrahedral number (or triangular pyramidal number).
Construction
A truncated pyramid is made when cut by a plane parallel to the base and the apical part is removed. The smaller truncated sections that are removed will always be similar to the larger, original shape.
The number to be removed (truncated) may be same or different from each of the vertices - but all numbers being removed would be a smaller Tetrahedral number (or triangular pyramidal number) by itself.
Properties
A truncated number is not the same as the volume of the truncated shape.
Examples
Tetrahedral Number 20 (sequence A000292 in the OEIS) yields Truncated Triangular Pyramid Number 7 (sequence A051937 in the OEIS) by truncating Tetrahedral number (or triangular pyramidal number) 4,4,4 and 1 from its vertices
Tetrahedral Number 35 (sequence A000292 in the OEIS) yields Truncated Triangular Pyramid Number 19 (sequence A051937 in the OEIS) by truncating Tetrahedral number (or triangular pyramidal number) 4 from each of the vertices
Tetrahedral Number 286 (sequence A000292 in the OEIS) yields Truncated Triangular Pyramid Number 273 (sequence A051937 in the OEIS) by truncating Tetrahedral number (or triangular pyramidal number) 4,4,4 and 1 from its vertices
Tetrahedral Number 560 (sequence A000292 in the OEIS) also yields Truncated Triangular Pyramid Number 273 (sequence A051937 in the OEIS) by truncating Tetrahedral number (or triangular pyramidal number) 84,84,84 and 35 from its vertices
Tetrahedral Number 816 (sequence A000292 in the OEIS) yields Truncated Triangular Pyramid Number 689 (sequence A051937 in the OEIS) by truncating Tetrahedral number (or triangular pyramidal number) 56,35,35 and 1 from its vertices
Tetrahedral Number 969 (sequence A000292 in the OEIS) yields Truncated Triangular Pyramid Number 833 (sequence A051937 in the OEIS) by truncating Tetrahedral number (or triangular pyramidal number) 56,35,35 and 10 from its vertices
Related numbers
Certain Truncated Triangular Pyramid Numbers may possess other characteristics too, like:
273 (number) is also a sphenic number and an idoneal number
204 (number) is also a square pyramidal number and a nonagonal number
In other fields
- Truncated triangular silver nanoplates synthesized in large quantities using a solution phase method[2]
- Theoretical study of hydrogen storage in a truncated triangular pyramid molecule[3]
- Packing and self-assembly of truncated triangular bipyramids[4]
References
- ^ Sloane, N. J. A. (ed.). "Sequence A051937 (Truncated triangular pyramid numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Chen, Sihai; Carroll, David L. (2002). "Synthesis and Characterization of Truncated Triangular Silver Nanoplates". Nano Letters. 2 (9): 1003–1007. Bibcode:2002NanoL...2.1003C. doi:10.1021/nl025674h.
- ^ Ishikawa, Shigeru; Nemoto, Tetsushi; Yamabe, Tokio (2018). "Theoretical study of hydrogen storage in a truncated triangular pyramid molecule consisting of pyridine and benzene rings bridged by vinylene groups". Applied Physics A. 124 (6): 418. Bibcode:2018ApPhA.124..418I. doi:10.1007/s00339-018-1841-9.
- ^ Haji-Akbari, Amir; Chen, Elizabeth R.; Engel, Michael; Glotzer, Sharon C. (2013). "Packing and self-assembly of truncated triangular bipyramids". Physical Review E. 88 (1): 012127. arXiv:1304.3147. Bibcode:2013PhRvE..88a2127H. doi:10.1103/PhysRevE.88.012127. PMID 23944434.