User:Peter Kagey

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
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]