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Codytized square tiling

Codytized square tiling

The codytized square tiling (codsquat) is an uncompact hyperbolic apeirocomb. It is the codytization of the square tiling.

Note: the 𝕱 polytopes are my naming. As far as I know, they do not have an official name besides their CD diagram.

Elements

Edges (1)

• Dyad x

Faces (1)

• Triangle x3o

Cells (2)

• Tetrahedron x3o3o

• Octahedron o3x3o

Tera (5)

Pentachoric symmetry (2)

• Pentachoron x3o3o3o

• Rectified pentachoron o3x3o3o

Demitesseractic symmetry (2)

• Hexadecachoron x3o3o *b3o

• Icositetrachoron o3x3o *b3o

Cyclotetrahedral honeycomb symmetry (1)

▪ Tetrahedral-octahedral honeycomb x3o3o3o3*a

Peta (13)

Hexateric symmetry (3)

• Hexateron x3o3o3o3o

• Rectified hexateron o3x3o3o3o

• Birectified hexateron o3o3x3o3o

Demipenteractic symmetry (4)

• Demipenteract x3o3o3o *b3o

• Penteractitriacontaditeron o3x3o3o *b3o

• Rectified triacontaditeron o3o3x3o *b3o

• Triacontaditeron o3o3o3x *b3o

Icositetrachoric tetracomb symmetry (2)

▪ Hexadecachoric tetracomb x3o3o *b3o *b3o

▪ Icositetrachoric tetracomb o3x3o *b3o *b3o

𝕱 symmetry (4)

▫ 𝕱¹ x3o3o3o3o3*b

▫ 𝕱² o3x3o3o3o3*b

▫ 𝕱³ o3o3x3o3o3*b

▫ 𝕱⁴ o3o3o3x3o3*b

Exa (35)

Heptapetic symmetry (3)

• Heptapeton x3o3o3o3o3o

• Rectified heptapeton o3x3o3o3o3o

• Birectified heptapeton o3o3x3o3o3o

Demihexeractic symmetry (5)

• Demihexeract x3o3o3o3o *b3o

• Birectified hexeract o3x3o3o3o *b3o

• Birectified hexacontatetrapeton o3o3x3o3o *b3o

• Rectified hexacontatetrapeton o3o3o3x3o *b3o

• Hexacontatetrapeton o3o3o3o3x *b3o

Pentacontatetrapetic symmetry (4)

• Icosiheptaheptacontadipeton x3o3o3o3o *c3o

• Rectified icosiheptaheptacontadipeton o3x3o3o3o *c3o

• Rectified pentacontatetrapeton o3o3x3o3o *c3o

• Pentacontatetrapeton o3o3o3o3o *c3x

Triacontaditeric pentacomb symmetry (4)

▫ Triacontaditeric pentacomb x3o3o3o *c3o *c3o

▫ Rectified pentacontaditeric pentacomb o3x3o3o *c3o *c3o

▫ Birectified pentacontaditeric pentacomb o3o3x3o *c3o *c3o

▫ 1₂₁₁ o3o3o3x *c3o *c3o

Demipenteractic pentacomb symmetry (2)

▪ Demipenteractic pentacomb x3o3o3o *b3o *c3o

▪ Birectified penteractic pentacomb o3x3o3o *b3o *c3o

𝕱₁ symmetry (5)

⁘ 𝕱₁¹ x3o3o3o3o3o3*c

⁘ 𝕱₁² o3x3o3o3o3o3*c

⁘ 𝕱₁³ o3o3x3o3o3o3*c

⁘ 𝕱₁⁴ o3o3o3x3o3o3*c

⁘ 𝕱₁⁵ o3o3o3o3x3o3*c

𝕱₂ symmetry (4)

⁘ 𝕱₂¹ x3o3o3o3o3*b3o

⁘ 𝕱₂² o3x3o3o3o3*b3o

⁘ 𝕱₂³ o3o3x3o3o3*b3o

⁘ 𝕱₂⁴ o3o3o3x3o3*b3o

𝕱₃ symmetry (3)

⁘ 𝕱₃¹ x3o3o3o3o3o *b3*e

⁘ 𝕱₃² o3x3o3o3o3o *b3*e

⁘ 𝕱₃³ o3o3x3o3o3o *b3*e

𝕱₆ symmetry (3)

⁘ 𝕱₆¹ x3o3o3o3o *b3o3*d

⁘ 𝕱₆² o3x3o3o3o *b3o3*d

⁘ 𝕱₆³ o3o3x3o3o *b3o3*d

𝕱₉ symmetry (2)

⁘ 𝕱₉¹ x3o3o3o3o3o3*a *b3*e

⁘ 𝕱₉² o3x3o3o3o3o3*a *b3*e