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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
snub cube
Hexagonal antiprism
Potentially embeddable anti/prisms
Triangular prism
Square prism (cube)
Hexagonal prism
Triangular antiprism (octahedron)
Square antiprism
Hexagonal antiprism
Potentially embeddable Johnson solids 
Number Name
1 Square pyramid
7 Elongated triangular pyramid
8 Elongated square pyramid
10 Gyroelongated square pyramid
12 Triangular bipyramid
13 Pentagonal bipyramid
14 Elongated triangular bipyramid
15 Elongated square bipyramid
16 Elongated pentagonal bipyramid
17 Gyroelongated square bipyramid
26 Gyrobifastigium
27 Triangular orthobicupola
28 Square orthobicupola
29 Square gyrobicupola
35 Elongated triangular orthobicupola
36 Elongated triangular gyrobicupola
37 Elongated square gyrobicupola
44 Gyroelongated triangular bicupola
45 Gyroelongated square bicupola
49 Augmented triangular prism
50 Biaugmented triangular prism
51 Triaugmented triangular prism
84 Snub disphenoid
85 Snub square antiprism
86 Sphenocorona
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]
Uniform
(Euclidean)
Snub Square A309159 [12]
Truncated square  ? [13]
Elongated triangular  ? [14]
Truncated Hexagonal  ? [15]
Trihexagonal tiling  ? [16]
Rhombitrihexagonal  ? [17]
Truncated trihexagonal  ? [18]
Snub trihexagonal  ? [19]
Other Rhombille tiling A197459 [20]
Higher
Dimensions
Cubic A038119 [21]
Tesseractic A068870 [22]
Hypercubic (k-D) A330891 [23]
Hypercubic (∞-D) A005519
Alternated Cubic  ? [24]