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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 (k-D) | 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] |