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. 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 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]