User:Tomruen/Regular product polytopes

Duo-forms

Regular product forms exist as honeycombs on a 3-sphere: {p,2,q}, with dihedral cells and hosohedral vertex figures. They are related to the 4D duoprisms where the square faces are flattened into rectangles and degenerated into digons.

Regular degenerate product polytopes as 3-sphere honeycombs
Schläfli {p,2,q}	Cells {p,2}_π/q	Faces {p}	Edges	Vertices	Vertex figure {2,q}	Symmetry	Dual
{p,2,2}	2 {p,2}	2 {p}	p	p	{2,2}_π/p	[p,2,2]	{2,2,p}
{2,2,2}	2 {2,2}	2 {2}	2	2	{2,2}_π/2	[2,2,2]	Self-dual
{3,2,2}	2 {3,2}	2 {3}	3	3	{2,2}_π/3	[3,2,2]	{2,2,p}
{p,2,p}	p {p,2}	p {p}	p	p	{2,p}_π/p	[p,2,p]	Self-dual
{3,2,3}	3 {3,2}	3 {3}	3	3	{2,3}_π/3	[3,2,3]	Self-dual
{p,2,q}	q {p,2}	q {p}	p	p	{2,q}_π/p	[p,2,q]	{q,2,p}
{4,2,3}	3 {4,2}	3 {4}	4	4	{2,3}_π/4	[4,2,3]	{3,2,4}

{2,p,2} = {2,2,p}

Regular degenerate product polytopes as 3-sphere honeycombs
Schläfli {2,p,2}	Coxeter	Cells {2,p}_π/p	Faces {2}_π/p,_π/2	Edges	Vertices	Vertex figure {p,2}	Symmetry	Dual
{2,p,2}		p {2,p}	p {2}	2	2	{p,2}	[2,p,2]	Self-dual
{2,3,2}		3 {2,3}	3 {2}	2	2	{3,2}	[2,3,2]	Self-dual

Ditopes and hosotopes

Regular di-4-topes (2 facets) include: {3,3,2}, {3,4,2}, {4,3,2}, {5,3,2}, {3,5,2}, and their hoso-4-tope duals (2 vertices): {2,3,3}, {2,4,3}, {2,3,4}, {2,3,5}, {2,5,3}.

Regular hoso-4-topes as 3-sphere honeycombs
Schläfli {2,p,q}	Cells {2,p}_π/q	Faces {2}_π/p,π/q	Edges	Vertices	Vertex figure {p,q}	Symmetry	Dual
{2,3,3}	4 {2,3}_π/3	6 {2}_π/3,π/3	4	2	{3,3}	[2,3,3]	{3,3,2}
{2,4,3}	6 {2,4}_π/3	12 {2}_π/4,π/3	8	2	{4,3}	[2,4,3]	{3,4,2}
{2,3,4}	8 {2,3}_π/4	12 {2}_π/3,π/4	6	2	{3,4}	[2,4,3]	{4,3,2}
{2,5,3}	12 {2,5}_π/3	30 {2}_π/5,π/3	20	2	{5,3}	[2,5,3]	{3,5,2}
{2,3,5}	20 {2,3}_π/5	30 {2}_π/3,π/5	12	2	{3,5}	[2,5,3]	{5,3,2}