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User:Peter Kagey

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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. In August 2017 I started a Ph.D. program at the University of Southern California.

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
rhombicuboctahedron (x and y adjacent on same square, z one of the corresponding vertices on opposite square.)
snub cube (degree 6 angle)
Potentially embeddable anti/prisms
Triangular prism
✓ Square prism (cube)
Hexagonal prism (Can be written as triangular prisms.
✓ Triangular antiprism (octahedron)
Square antiprism (Angle between x, y adjacent to x on same square, z on same triangle as x but not same as y, does not have quadratic root cosine.)
Hexagonal antiprism (Angle between x, y adjacent to x on other hexagon, z opposite x on x's hexagon, does not have quadratic root cosine.)
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 Elongated triangular cupola (2,5,10; degree 4)
22 Gyroelongated triangular cupola (2,5,10; degree 8)
26 Gyrobifastigium
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 Augmented hexagonal prism (1,2,13; degree 4)
55 Parabiaugmented hexagonal prism (1,5,13; degree 4)
56 Metabiaugmented hexagonal prism ((1,10,13; degree 4)
57 Triaugmented hexagonal prism ((7,10,13; degree 4)
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]