This site is supported by donations to The OEIS Foundation.
User:Peter Kagey
From OeisWiki
I graduated from Oregon State University in June 2014 with a B.S. in Mathematics. From December 2014 until August 2017, I worked as a back end web engineer at a health technology company. From August 2017–July 2022, I was in a Ph.D. program at the University of Southern California. From 2022–2024, I am a visiting assistant professor at Harvey Mudd College.
Most of the scripts that I have written to generate OEIS sequences can be found on my OEIS Github Repository. I work mostly in Haskell.
Feel free to contact me at peterkagey@gmail.com or on LinkedIn.
Polytopes in lattices
Polygons in lattices  

2D  3D  
Square  Rectangular  Centered Square  Triangular  Centered Hexagonal  Cubic  Tetrahedral  Octahedral  
Equilateral Triangle        A000332  A008893  A102698  A334581*  ? 
Square  A002415  A130684  A006324      A334881*  A334891*  ? 
Regular Hexagon        A011779 (?)  A000537  A338322*  ?  ? 
Regular Polygon  A002415  A130684  A006324  ?  A339483*  A338323*  ?  ? 
Triangle  A045996  A334705  ?  ?  A241223  ?  ?  ? 
Rectangle  A085582  A289832  ?      ?  ?  ? 
Right Triangle  A077435  ?  ?  ?  A241225  ?  ?  ? 
Other polygons in lattices  

Square  Rectangular  Centered Hexagonal  Centered Square  Triangular  
Acute Triangle  A190019  A241224  
Obtuse Triangle  A190020  A241226  
Scalene Triangle  A190312  A241227  
Isosceles Triangle  A186434  A271910  A241228  
Acute Isosceles  A190317  A272625  A241229  
Obtuse Isosceles  A190318  A272624  A241230  
Concave Quadrilateral  A189412  
Convex Quadrilateral  A189413  
Quadrilateral  A189414  
Trapezoid  A189415  
Parallelogram  A189416  
Kite  A189417  
Rhombus  A189418 
Polyhedra in lattices  

Cubic  Tetrahedral  Octahedral  
Regular Tetrahedron  A103158  A269747  ? 
Cube  A098928  ?  ? 
Octahedron  A178797  ?  ? 
Platonic Solid  A338791  ?  ? 
Potentially embeddable Archimedean solids 

✓ truncated tetrahedron 
✓ cuboctahedron 
✓ truncated octahedron 


Potentially embeddable anti/prisms 


✓ Square prism (cube) 

✓ Triangular antiprism (octahedron) 


Potentially embeddable Johnson solids  

Number  Name 
1  ✓ Square pyramid (half an octahedron) 
3  ✓ Triangular cupola (half a cuboctahedron) 
12  ✓ Triangular bipyramid {(0,0,0), (3,3,0), (3,0,3), (0,3,3), (4,4,4)} 
18  
22  
26  
27  ✓ Triangular orthobicupola {(0,3,3), (3,0,3), (3,3,0), (0,3,3), (3,0,3), (3,3,0), (0,3,3), (3,0,3), (3,3,0), (4,1,1), (1,4,1), (1,1,4)} 
54  
55  
56  
57  
65  ✓ Augmented truncated tetrahedron {(0,3,3), (3,0,3), (3,3,0), (0,6,6), (6,0,6), (6,6,0), (3,6,9), (6,9,3), (9,3,6), (3,9,6), (6,3,9), (9,6,3), (10,7,7), (7,10,7), (7,7,10)} 
87  Augmented sphenocorona? 
88  Sphenomegacorona? 
89  Hebesphenomegacorona? 
90  Disphenocingulum? 
Polyforms on tilings
Family  Tiling  Sequence  Link 

Regular (Euclidean) 
Square ({4,4})  A000105  [1] 
Hexagonal ({6,3})  A000228  [2]  
Triangular ({3,6})  A000577  [3]  
Regular (hyperbolic) 
{3,7} (hyperbolic)  A330659  [4] 
{3,∞} (hyperbolic)  A000207  [5]  
{4,5} (hyperbolic)  A119611  [6]  
{4,6} (hyperbolic)  A332930  [7]  
{4,∞} (hyperbolic)  A005036  [8]  
{5,4} (hyperbolic)  A330211  [9]  
{7,3} (hyperbolic)  A333018  [10]  
{k,∞} (hyperbolic)  A295260  [11]  
Higher Dimensions 
Cubic  A038119  [12] 
Tesseractic  A068870  [13]  
Hypercubic (kD)  A330891  [14]  
Hypercubic (∞D)  A005519  
Alternated Cubic  A343909  [15] 
Uniform Tiling  Sequence  Link  Dual tiling  Sequence  Link 

Snub Square  A309159  [16]  Cairo pentagonal tiling  ?  [17] 
Truncated square  A343577  [18]  Tetrakis square tiling  A197465  [19] 
Elongated triangular  A345076  [20]  Prismatic pentagonal tiling  A197156  [21] 
Truncated hexagonal  A343406  [22]  Triakis triangular tiling  ?  [23] 
Trihexagonal tiling  A343398  [24]  Rhombille tiling  A197459  [25] 
Rhombitrihexagonal  A344211  [26]  Deltoidal trihexagonal tiling  ?  [27] 
Truncated trihexagonal  A344213  [28]  Kishombille tiling  A197462  [29] 
Snub trihexagonal  ?  [30]  Floret pentagonal tiling  A197159  [31] 