### Euclidean Tesselations

• 1D Tesselations (Sequence)
• 2D Tesselations (Tilings)
• 3D Tesselations (Honeycombs)
• 4D Tesselations (Tetracombs)
• 5D Tesselations (Pentacombs)
• 6D Tesselations (Hexacombs)
• 7D Tesselations (Heptacombs)
• 8D Tesselations (Octacombs)

As a foregoing consideration one might ask whether euclidean space curvature also does allow for non-simplicial reflection groups, such as the hyperbolic one does. In fact, one should state, that this is the case here indeed. But, on the other hand, that extraordinary regime of varities breaks down in here to one rather tame effect: For D=2 we just can have a tetragonal fundamental domain, with all angles being α=π/2, i.e. a rectangle. In Weyl notation that "extraordinary" symmetry is nothing but A1×A1.

For higher dimensions this same effect generalizes to cartesian honeycomb products of lower dimensional euclidean tesselations, where the fundamental domains derive likewise by orthogonal prism products of those of the factor tesselations. In terms of symmetries this generally is called a reducible (afine) symmetry. In Weyl group description those are marked by an ×.

Just as in hyperbolic geometry, non-simplicial reflection groups in here also provide some additional degrees of freedom: a reducible symmetry with n factors, allows for n-1 independent relative scalings of the orthogonal factor domains. (Sure, the absolut size of the first factor in euclidean space is not restricted either.)

Euclidean tesselations are closely related to cell complexes based on lattices. Best known is the Voronoi complex. This is an isohedral (1 single cell class) tesselation of space. Each cell is the closure of all points nearer to any specific lattice point than to any other.

The locally dual complex is the Delone complex. The vertices thus are the lattice points again. Two lattice points are joined by an edge iff the corresponding Voronoi cells are adjoined at an facet, etc. There might be several different types of Delone cells, corresponding to the symmetry inequivalent types of vertices of the Voronoi cell. Both these complexes by definition use convex cells only.

Beside to the (unmarked) Dynkin symbols of the symmetry groups the corresponding representations as Weyl groups and as Coxeter groups are given.

Finally, besides of (marked) Dynkin symbols and Bowers acronyms for individual tesselations (up to dimension 4) the Olshevsky numbers ("O...") are provided as well. Those refer onto his paper on Uniform Panoploid Tetracombs, assembled since 2003, made available in 2006.)

```----
1D  Sequence (up)
----
```
 o∞o = A1 = W(2) ```x∞o - aze x∞x - aze ```

The full name of this infinite-gon (with acronym aze) is apeirogon.

A1, taken as lattice, defines the intervals inbetween as Delone cells, while the Voronoi cells are those intervals shifted by half a unit length. Both complexes are equivalent (relatively shifted) to the apeirogon.

```----
2D  Tilings (up)
----
```
 o3o6o = G2 = V(3) o4o4o = C2 = R(3) o3o3o3*a = A2 = P(3) o∞o o∞o = A1×A1 = W(2)2 ```x3o6o - trat - O2 o3x6o - that - O5 o3o6x - hexat - O3 x3x6o - hexat - O3 x3o6x - rothat - O8 o3x6x - toxat - O7 x3x6x - othat - O9 ``` ```x4o4o - squat - O1 o4x4o - squat - O1 x4x4o - tosquat - O6 x4o4x - squat - O1 x4x4x - tosquat - O6 ``` ```x3o3o3*a - trat - O2 x3x3o3*a - that - O5 x3x3x3*a - hexat - O3 ``` ```x∞o x∞o - squat - O1 x∞x x∞o - squat - O1 x∞x x∞x - squat - O1 ``` snubs of o3o6o snubs of o4o4o snubs of o3o3o3*a other uniforms ```s6o3o - trat - O2 s6x3o - that - O5 s6o3x - that - O5 s6x3x - hexat - O3 s3s6o - trat - O2 s3s6x - rothat - O8 s3s6s - snathat - O11 β6β3o - 2that+∞{3} (?) β6β3x - 2rothat (?) β3x6o - 2that (?) β3o6x - shothat β3x6x - 2toxat (?) x3β6x - 2rothat (?) ``` ```s4o4o - squat - O1 s4x4o - squat - O1 s4o4x - tosquat - O6 s4x4x - tosquat - O6 o4s4o - squat - O1 x4s4o - squat - O1 x4s4x - squat - O1 s4s4o - snasquat - O10 s4s4x - squat - O1 s4o4s - squat - O1 s4x4s - squat - O1 s4s4s - snasquat - O10 s4o4s' - snasquat - O10 s4x4s' - squat - O1 ss'4o4x - squat - O1 ``` ```s3s3s3*a - trat - O2 ``` ```elong( x3o6o ) - etrat - O4 x6x3/2o6*a - shothat hemi( ? ) - ditatha hemi( ? ) - tha hemi( ? ) - hoha hemi( ? ) - sha x∞o x - azip x∞x x - azip s∞o2s - azap s∞s2s - azap ```

As lattice A2 and G2 are equivalent. The Voronoi cell is the hexagon, the Delone cell is the regular triangle. The Voronoi complex is hexat, the Delonai complex is trat.

The lattice C2 clearly has squares for Voronoi and Delone cells. Both complexes are relatively shifted representants of squat.

(A nice applet for experimental tiling of the 2D euclidean plane (as well as hyperbolic ones) is tyler.)

```----
3D  Honeycombs (up)
----
```
 o4o3o4o = C3 = R(4) o3o3o *b4o = B3 = S(4) o3o3o3o3*a = A3 = P(4) o∞o o3o6o = A1×G2 = W(2)×V(3) ```x4o3o4o - chon - O1 o4x3o4o - rich - O15 x4x3o4o - tich - O14 x4o3x4o - srich - O17 x4o3o4x - chon - O1 o4x3x4o - batch - O16 x4x3x4o - grich - O18 x4x3o4x - prich - O19 x4x3x4x - otch - O20 ``` ```x3o3o *b4o - octet - O21 o3x3o *b4o - rich - O15 o3o3o *b4x - chon - O1 x3x3o *b4o - tatoh - O25 x3o3x *b4o - rich - O15 x3o3o *b4x - ratoh - O26 o3x3o *b4x - tich - O14 x3x3x *b4o - batch - O16 x3x3o *b4x - gratoh - O28 x3o3x *b4x - srich - O17 x3x3x *b4x - grich - O18 ``` ```x3o3o3o3*a - octet - O21 x3x3o3o3*a - batatoh - O27 x3o3x3o3*a - rich - O15 x3x3x3o3*a - tatoh - O25 x3x3x3x3*a - batch - O16 ``` ```x∞o x3o6o - tiph - O2 x∞o o3x6o - thiph - O5 x∞o o3o6x - hiph - O3 x∞x x3o6o - tiph - O2 x∞x o3x6o - thiph - O5 x∞x o3o6x - hiph - O3 x∞o x3x6o - hiph - O3 x∞o x3o6x - rothaph - O8 x∞o o3x6x - thaph - O7 x∞x x3x6o - hiph - O3 x∞x x3o6x - rothaph - O8 x∞x o3x6x - thaph - O7 x∞o x3x6x - otathaph - O9 x∞x x3x6x - otathaph - O9 x∞o s3s6s - snathaph - O11 x∞x s3s6s - snathaph - O11 ``` o∞o o4o4o = A1×C2 = W(2)×R(3) o∞o o3o3o3*c = A1×A2 = W(2)×P(3) o∞o o∞o o∞o = A1×A1×A1 = W(2)3 other uniforms ```x∞o x4o4o - chon - O1 x∞o o4x4o - chon - O1 x∞x x4o4o - chon - O1 x∞x o4x4o - chon - O1 x∞o x4x4o - tassiph - O6 x∞o x4o4x - chon - O1 x∞x x4x4o - tassiph - O6 x∞x x4o4x - chon - O1 x∞o x4x4x - tassiph - O6 x∞x x4x4x - tassiph - O6 x∞o s4s4s - sassiph - O10 x∞x s4s4s - sassiph - O10 ``` ```x∞o x3o3o3*c - tiph - O2 x∞x x3o3o3*c - tiph - O2 x∞o x3x3o3*c - thiph - O5 x∞x x3x3o3*c - thiph - O5 x∞o x3x3x3*c - hiph - O3 x∞x x3x3x3*c - hiph - O3 x∞o s3s3s3*c - tiph - O2 x∞x s3s3s3*c - tiph - O2 ``` ```x∞o x∞o x∞o - chon - O1 x∞x x∞o x∞o - chon - O1 x∞x x∞x x∞o - chon - O1 x∞x x∞x x∞x - chon - O1 ``` ```gyro( x3o3o3o3*a ) - gytoh - O22 elong( x3o3o3o3*a ) - etoh - O23 gyroelong( x3o3o3o3*a ) - gyetoh - O24 gyro( x3o3o *b4o ) - gytoh - O22 elong( x3o3o *b4o ) - etoh - O23 gyroelong( x3o3o *b4o ) - gyetoh - O24 gyro( x∞o x3o6o ) - gytoph - O12 elong( x∞o x3o6o ) - etoph - O4 gyroelong( x∞o x3o6o ) - gyetaph - O13 x∞o elong( x3o6o ) - etoph - O4 x∞x elong( x3o6o ) - etoph - O4 gyro( x∞o x3o3o3*c ) - gytoph - O12 elong( x∞o x3o3o3*c ) - etoph - O4 gyroelong( x∞o x3o3o3*c ) - gyetaph - O13 x∞o elong( x3o3o3*c ) - etoph - O4 x∞x elong( x3o3o3*c ) - etoph - O4 x∞o x-n-o - n-azedip x∞x x-n-o - n-azedip x∞x s-n-s - n-azedip ```

In 3D there are several different lattices, known as the Bravais lattices of crystallography. Only the higher symmetrical ones are related to uniform tesselations. As lattices A1×G2 and A1×A2 again are equivalent, the Voronoi complex of it is hiph, the Delone complex is tiph.

In the cubical area there are 3 different lattices. First there is the primitive cubical one, C3. Its Voronoi complex and its Delone complex both are relatively shifted chon.

Next there is the body-centered cubical (bcc) lattice. Thus it is the union of the primitive cubical lattice plus its Voronoi cell vertices ("holes"). The Voronoi complex here is batch. The Delone cells are non-uniform digonal antiprisms.

Finally there is the face-centered cubical (fcc) lattice, as lattice equivalently derived from A3 or B3, and alternatively described as mod 2 of the sum of the vertex coordinates of a (smaller) primitive cubical lattice. Its Voronoi cell is the rhombic dodecahedron (rad). The Delone complex is octet, with 2 different Delone cells, oct corresponding to the 4-fold vertices of rad ("deep holes"), while tet corresponds to the 3-fold vertices of rad ("shallow holes").

```----
4D  Tetracombs (up)
----
```
 o4o3o3o4o = C4 = R(5) o3o3o *b3o4o = B4 = S(5) o3o3o *b3o *b3o = D4 = Q(5) o3o3o3o3o3*a = A4 = P(5) ```x4o3o3o4o - test - O1 o4x3o3o4o - rittit - O87 o4o3x3o4o - icot - O88 x4x3o3o4o - tattit - O89 x4o3x3o4o - srittit - O90 x4o3o3x4o - sidpitit - O91 x4o3o3o4x - test - O1 o4x3x3o4o - batitit - O92 o4x3o3x4o - ricot - O93 x4x3x3o4o - grittit - O94 great prismatotesseractic TC x4x3o3x4o - potatit - O95 prismatotruncated tesseractic TC, small tomocubic-diprismatotesseractic TC x4x3o3o4x - capotat - O96 celliprismated tesseractic TC, tomotesseractic-diprismatotesseractic TC x4o3x3x4o - prittit - O97 prismatorhombated tesseractic TC, rhombitesseractic-diprismatotesseractic TC x4o3x3o4x - scartit - O98 small cellirhombated tesseractic TC, small rhombitesseractic-prismatotesseractic TC o4x3x3x4o - ticot - O99 truncated icositetrachoric TC x4x3x3x4o - gippittit - O100 great prismated tesseractic TC, great diprismatotesseractic TC x4x3x3o4x - gicartit - O101 great cellirhombated tesseractic TC, great rhombitesseractic-prismatotesseractic TC x4x3o3x4x - captatit - O102 celliprismatotruncated tesseractic TC, great tomocubic-diprismatotesseractic TC x4x3x3x4x - otatit - O103 omnitruncated tesseractic TC s4o3o3o4o - hext - O104 o4s3s3s4o - sadit - O133 ``` ```x3o3o *b3o4o - hext - O104 o3x3o *b3o4o - icot - O88 o3o3o *b3x4o - rittit - O87 o3o3o *b3o4x - test - O1 x3x3o *b3o4o - thext - O105 x3o3x *b3o4o - rittit - O87 x3o3o *b3x4o - bricot - O106 x3o3o *b3o4x - siphatit - O108 small diprismatodemitesseractic TC o3x3o *b3x4o - batitit - O92 o3x3o *b3o4x - srittit - O90 o3o3o *b3x4x - tattit - O89 x3x3x *b3o4o - batitit - O92 x3x3o *b3x4o - bithit - O107 bitruncated hexadecachoric TC, bitruncated demitesseractic TC x3x3o *b3o4x - pithatit - O109 prismatotruncated demitesseractic TC, small prismatodemitesseractic TC x3o3x *b3x4o - ricot - O93 x3o3x *b3o4x - sidpitit - O91 x3o3o *b3x4x - pirhatit - O110 prismatorhombated demitesseractic TC, great prismatodemitesseractic TC o3x3o *b3x4x - grittit - O94 x3x3x *b3x4o - ticot - O99 x3x3x *b3o4x - prittit - O97 x3x3o *b3x4x - giphatit - O111 great prismated demitesseractic TC, great diprismatodemitesseractic TC x3o3x *b3x4x - potatit - O95 x3x3x *b3x4x - gippittit - O100 s3s3s *b3s4o - sadit - O133 ``` ```x3o3o *b3o *b3o - hext - O104 o3x3o *b3o *b3o - icot - O88 x3x3o *b3o *b3o - thext - O105 x3o3x *b3o *b3o - rittit - O87 x3x3x *b3o *b3o - batitit - O92 x3o3x *b3x *b3o - bricot - O106 x3x3x *b3x *b3o - bithit - O107 x3o3x *b3x *b3x - ricot - O93 x3x3x *b3x *b3x - ticot - O99 s3s3s *b3s *b3s - sadit - O133 ``` ```x3o3o3o3o3*a - cypit - O134 x3x3o3o3o3*a - cytopit - O135 x3o3x3o3o3*a - scyropot - O136 x3x3x3o3o3*a - gocyropit - O137 great cyclorhombated pentachoric TC, great truncated-pentachoric TC x3x3o3x3o3*a - cypropit - O138 x3x3x3x3o3*a - gocypapit - O139 great cycloprismated pentachoric TC, grand prismatodispentachoric TC x3x3x3x3x3*a - otcypit - O140 ``` o3o3o4o3o = F4 = U(5) o∞o o4o3o4o = A1×C3 = W(2)×R(4) o∞o o3o3o *d4o = A1×B3 = W(2)×S(4) o∞o o3o3o3o3*c = A1×A3 = W(2)×P(4) ```x3o3o4o3o - hext - O104 o3x3o4o3o - icot - O88 o3o3x4o3o - bricot - O106 o3o3o4x3o - ricot - O93 o3o3o4o3x - icot - O88 x3x3o4o3o - thext - O105 x3o3x4o3o - ricot - O93 x3o3o4x3o - spaht - O122 small prismated demitesseractic TC, small disicositetrachoric TC x3o3o4o3x - scicot - O121 small cellated icositetrachoric TC, runcinated icositetrachoric TC o3x3x4o3o - bithit - O107 o3x3o4x3o - sibricot - O116 small birhombated icositetrachoric TC, grand prismatodisicositetrachoric TC o3x3o4o3x - spict - O115 small prismated icositetrachoric TC, small prismatotetracontaoctachoric TC o3o3x4x3o - baticot - O113 bitruncated icositetrachoric TC, small tetracontaoctachoric TC o3o3x4o3x - sricot - O112 small rhombated icositetrachoric TC, small prismatodisicositetrachoric TC o3o3o4x3x - ticot - O99 x3x3x4o3o - ticot - O99 x3x3o4x3o - pataht - O128 prismatotruncated demitesseractic TC, prismatodiprismatodisicositetrachoric TC x3x3o4o3x - capicot - O127 celliprismated icositetrachoric TC, great prismatotetracontaoctachoric TC x3o3x4x3o - praht - O125 prismatorhombated demitesseractic TC, great tetracontaoctachoric TC x3o3x4o3x - scaricot - O124 small cellirhombated icositetrachoric TC, great disicositetrachoric TC x3o3o4x3x - capoht - O123 celliprismated demitesseractic TC, tomoicositetrachoric-diprismatotesseractic TC o3x3x4x3o - gibricot - O119 great birhombated icositetrachoric TC, great grand prismatodisicositetrachoric TC o3x3x4o3x - pricot - O118 prismatorhombated icositetrachoric TC, great diprismatodisicositetrachoric TC o3x3o4x3x - paticot - O117 prismatotruncated icositetrachoric TC, small diprismatodisicositetrachoric TC o3o3x4x3x - gricot - O114 great rhombated icositetrachoric TC, great prismatodisicositetrachoric TC x3x3x4x3o - gipaht - O131 great prismated demitesseractic TC x3x3x4o3x - gicaricot - O130 great cellirhombated icositetrachoric TC, runcicantic hexadecachoric TC x3x3o4x3x - capticot - O129 celliprismatotruncated icositetrachoric TC x3o3x4x3x - gicaroht - O126 great cellirhombated demitesseractic TC, runcicantic icositetrachoric TC o3x3x4x3x - gippict - O120 great prismated icositetrachoric TC x3x3x4x3x - otit - O132 omnitruncated icositetrachoric TC o3o3o4s3s - sadit - O133 s3s3s4o3o - sadit - O133 ``` ```x∞o x4o3o4o - test - O1 x∞o o4x3o4o - ricpit - O15 rectified-cubic prismatic TC x∞x x4o3o4o - test - O1 x∞x o4x3o4o - ricpit - O15 x∞o x4x3o4o - ticpit - O14 truncated-cubic prismatic TC x∞o x4o3x4o - cacpit - O17 cantellated-cubic prismatic TC x∞o x4o3o4x - test - O1 x∞o o4x3x4o - bitticpit - O16 bitruncated-cubic prismatic TC x∞x x4x3o4o - ticpit - O14 x∞x x4o3x4o - cacpit - O17 x∞x x4o3o4x - test - O1 x∞x o4x3x4o - bitticpit - O16 x∞o x4x3x4o - catcupit - O18 cantitruncated-cubic prismatic TC x∞o x4x3o4x - rutcupit - O19 runcitruncated-cubic prismatic TC x∞x x4x3x4o - catcupit - O18 x∞x x4x3o4x - rutcupit - O19 x∞o x4x3x4x - otacpit - O20 omnitruncated-cubic prismatic TC x∞x x4x3x4x - otacpit - O20 ``` ```x∞o x3o3o *d4o - acpit - O21 alternated-cubic prismatic TC x∞o o3x3o *d4o - ricpit - O15 x∞o o3o3o *d4x - test - O1 x∞x x3o3o *d4o - acpit - O21 x∞x o3x3o *d4o - ricpit - O15 x∞x o3o3o *d4x - test - O1 x∞o x3x3o *d4o - tacpit - O25 truncated-alternated-cubic prismatic TC x∞o x3o3x *d4o - ricpit - O15 x∞o x3o3o *d4x - racpit - O26 runcinated-alternated-cubic prismatic TC x∞o o3x3o *d4x - ticpit - O14 x∞x x3x3o *d4o - tacpit - O25 x∞x x3o3x *d4o - ricpit - O15 x∞x x3o3o *d4x - racpit - O26 x∞x o3x3o *d4x - ticpit - O14 x∞o x3x3x *d4o - bitticpit - O16 x∞o x3x3o *d4x - rucacpit - O28 runcicantic-cubic prismatic TC x∞o x3o3x *d4x - cacpit - O17 x∞x x3x3x *d4o - bitticpit - O16 x∞x x3x3o *d4x - rucacpit - O28 x∞x x3o3x *d4x - cacpit - O17 x∞o x3x3x *d4x - catcupit - O18 x∞x x3x3x *d4x - catcupit - O18 ``` ```x∞o x3o3o3o3*c - acpit - O21 x∞x x3o3o3o3*c - acpit - O21 x∞o x3x3o3o3*c - quacpit - O27 quarter-cubic prismatic TC x∞o x3o3x3o3*c - ricpit - O15 x∞x x3x3o3o3*c - quacpit - O27 x∞x x3o3x3o3*c - ricpit - O15 x∞o x3x3x3o3*c - tacpit - O25 x∞x x3x3x3o3*c - tacpit - O25 x∞o x3x3x3x3*c - bitticpit - O16 x∞x x3x3x3x3*c - bitticpit - O16 ``` o3o6o o3o6o = G2×G2 = V(3)2 o3o6o o4o4o = G2×C2 = V(3)×R(3) o3o6o o3o3o3*d = G2×A2 = V(3)×P(3) o4o4o o4o4o = C2×C2 = R(3)2 ```x3o6o x3o6o - tribbit - O29 x3o6o o3x6o - tathibbit - O32 triangular-trihexagonal duoprismatic TC x3o6o o3o6x - thibbit - O30 triangular-hexagonal duoprismatic TC o3x6o o3x6o - thabbit - O56 trihexagonal duoprismatic TC o3x6o o3o6x - hithibbit - O41 hexagonal-trihexagonal duoprismatic TC o3o6x o3o6x - hibbit - O39 hexagonal duoprismatic TC x3x6o x3o6o - thibbit - O30 x3x6o o3x6o - hithibbit - O41 x3x6o o3o6x - hibbit - O39 x3o6x x3o6o - trithit - O35 triangular-rhombitrihexagonal TC x3o6x o3x6o - thrathibbit - O59 x3o6x o3o6x - harhibit - O44 hexagonal-rhombihexagonal duoprismatic TC o3x6x x3o6o - tathobit - O34 triangular-tomohexagonal duoprismatic TC o3x6x o3x6o - thathobit - O58 trihexagonal-tomohexagonal duoprismatic TC o3x6x o3o6x - hithobit - O43 hexagonal-tomohexagonal duoprismatic TC x3x6x x3o6o - totuthit - O36 triangular-omnitruncated-trihexagonal TC x3x6x o3x6o - thot thibbit - O60 x3x6x o3o6x - hot thibbit - O45 x3x6o x3x6o - hibbit - O39 x3x6o x3o6x - harhibit - O44 x3x6o o3x6x - hithobit - O43 x3o6x x3o6x - rithbit - O74 rhombitrihexagonal duoprismatic TC x3o6x o3x6x - thorahbit - O70 o3x6x o3x6x - thobit - O69 tomohexagonal duoprismatic TC x3x6x x3x6o - hot thibbit - O45 x3x6x x3o6x - rathotathibit - O75 x3x6x o3x6x - thoot thibbit - O71 x3x6x x3x6x - otathibbit - O78 omnitruncated-trihexagonal duoprismatic TC x3o6o s3s6s - tisthit - O38 o3x6o s3s6s - thisthibbit - O62 trihexagonal-simotrihexagonal duoprismatic TC o3o6x s3s6s - hasithbit - O47 hexagonal-simotrihexagonal duoprismatic TC x3x6o s3s6s - hasithbit - O47 x3o6x s3s6s - rithsithbit - O77 o3x6x s3s6s - thosithbit - O73 tomohexagonal-simotrihexagonal duoprismatic TC x3x6x s3s6s - otsithbit - O80 omnitruncated-simotrihexagonal duoprismatic TC s3s6s s3s6s - sithbit - O83 simotrihexagonal duoprismatic TC ``` ```x3o6o x4o4o - tisbat - O2 triangular-square duoprismatic TC x3o6o o4x4o - tisbat - O2 o3x6o x4o4o - thisbit - O5 trihexagonal-square duoprismatic TC o3x6o o4x4o - thisbit - O5 o3o6x x4o4o - shibbit - O3 square-hexagonal duoprismatic TC o3o6x o4x4o - shibbit - O3 x3x6o x4o4o - shibbit - O3 x3x6o o4x4o - shibbit - O3 x3o6x x4o4o - rithsibbit - O8 rhombitrihexagonal-square duoprismatic TC x3o6x o4x4o - rithsibbit - O8 o3x6x x4o4o - thosbit - O7 tomohexagonal-square duoprismatic TC o3x6x o4x4o - thosbit - O7 x3o6o x4x4o - tatosbit - O33 triangular-tomosquare duoprismatic TC x3o6o x4o4x - tisbat - O2 o3x6o x4x4o - thatosbit - O57 trihexagonal-tomosquare duoprismatic TC o3x6o x4o4x - thisbit - O5 o3o6x x4x4o - hitosbit - O42 hexagonal-tomosquare duoprismatic TC o3o6x x4o4x - shibbit - O3 x3x6x x4o4o - otathisbit - O9 x3x6x o4x4o - otathisbit - O9 x3x6o x4x4o - hitosbit - O42 x3x6o x4o4x - shibbit - O3 x3o6x x4x4o - tosrithbit - O65 tomosquare-rhombitrihexagonal duoprismatic TC x3o6x x4o4x - rithsibbit - O8 o3x6x x4x4o - tosthobit - O64 tomosquare-tomohexagonal duoprismatic TC o3x6x x4o4x - thosbit - O7 x3o6o x4x4x - tatosbit - O33 o3x6o x4x4x - thatosbit - O57 o3o6x x4x4x - hitosbit - O42 x3x6x x4x4o - tosot thibbit - O66 x3x6x x4o4x - otathisbit - O9 x3x6o x4x4x - hitosbit - O42 x3o6x x4x4x - tosrithbit - O65 o3x6x x4x4x - tosthobit - O64 x3x6x x4x4x - tosot thibbit - O66 x3o6o s4s4s - tasist - O37 triangular-simosquare TC o3x6o s4s4s - thisosbit - O61 trihexagonal-simosquare duoprismatic TC o3o6x s4s4s - hisosbit - O46 hexagonal-simosquare duoprismatic TC x3x6o s4s4s - hisosbit - O46 x3o6x s4s4s - rithsisbit - O76 rhombitrihexagonal-simosquare duoprismatic TC o3x6x s4s4s - thosisbit - O72 tomohexagonal-simosquare duoprismatic TC x3x6x s4s4s - otsisbit - O79 omnitruncated-simosquare duoprismatic TC s3s6s x4o4o - sithsobit - O11 simotrihexagonal-square duoprismatic TC s3s6s o4x4o - sithsobit - O11 s3s6s x4x4o - tosasithbit - O68 tomosquare-simotrihexagonal duoprismatic TC s3s6s x4o4x - sithsobit - O11 s3s6s x4x4x - tosasithbit - O68 s3s6s s4s4s - sissithbit - O82 simosquare-simotrihexagonal duoprismatic TC ``` ```x3o6o x3o3o3*d - tribbit - O29 o3x6o x3o3o3*d - tathibbit - O32 o3o6x x3o3o3*d - thibbit - O30 x3x6o x3o3o3*d - thibbit - O30 x3o6x x3o3o3*d - trithit - O35 o3x6x x3o3o3*d - tathobit - O34 x3o6o x3x3o3*d - tathibbit - O32 o3x6o x3x3o3*d - thabbit - O56 o3o6x x3x3o3*d - hithibbit - O41 x3x6x x3o3o3*d - totuthit - O36 x3x6o x3x3o3*d - hithibbit - O41 x3o6x x3x3o3*d - thrathibbit - O59 o3x6x x3x3o3*d - thathobit - O58 x3o6o x3x3x3*d - thibbit - O30 o3x6o x3x3x3*d - hithibbit - O41 o3o6x x3x3x3*d - hibbit - O39 x3x6x x3x3o3*d - thot thibbit - O60 x3x6o x3x3x3*d - hibbit - O39 x3o6x x3x3x3*d - harhibit - O44 o3x6x x3x3x3*d - hithobit - O43 x3x6x x3x3x3*d - hot thibbit - O45 s3s6s x3o3o3*d - tisthit - O38 s3s6s x3x3o3*d - thisthibbit - O62 s3s6s x3x3x3*d - hasithbit - O47 ``` ```x4o4o x4o4o - test - O1 x4o4o o4x4o - test - O1 o4x4o o4x4o - test - O1 x4x4o x4o4o - tososbit - O6 tomosquare-square duoprismatic TC x4x4o o4x4o - tososbit - O6 x4o4x x4o4o - test - O1 x4o4x o4x4o - test - O1 x4x4x x4o4o - tososbit - O6 x4x4x o4x4o - tososbit - O6 x4x4o x4x4o - tosbit - O63 tomosquare duoprismatic TC x4x4o x4o4x - tososbit - O6 x4o4x x4o4x - test - O1 x4x4x x4x4o - tosbit - O63 x4x4x x4o4x - tososbit - O6 x4x4x x4x4x - tosbit - O63 s4s4s x4o4o - sisosbit - O10 simosquare-square duoprismatic TC s4s4s o4x4o - sisosbit - O10 s4s4s x4x4o - tosisasbit - O67 tomosquare-simosquare duoprismatic TC s4s4s x4o4x - sisosbit - O10 s4s4s x4x4x - tosisasbit - O67 s4s4s s4s4s - sisbit - O81 simosquare duoprismatic TC ``` o4o4o o3o3o3*d = C2×A2 = R(3)×P(3) o3o3o3*a o3o3o3*d = A2×A2 = P(3)2 o∞o o∞o o3o6o = A1×A1×G2 = W(2)2×V(3) o∞o o∞o o4o4o = A1×A1×C2 = W(2)2×R(3) ```x4o4o x3o3o3*d - tisbat - O2 o4x4o x3o3o3*d - tisbat - O2 x4x4o x3o3o3*d - tatosbit - O33 x4o4x x3o3o3*d - tisbat - O2 x4o4o x3x3o3*d - thisbit - O5 o4x4o x3x3o3*d - thisbit - O5 x4x4x x3o3o3*d - tatosbit - O33 x4x4o x3x3o3*d - thatosbit - O57 x4o4x x3x3o3*d - thisbit - O5 x4o4o x3x3x3*d - shibbit - O3 o4x4o x3x3x3*d - shibbit - O3 x4x4x x3x3o3*d - thatosbit - O57 x4x4o x3x3x3*d - hitosbit - O42 x4o4x x3x3x3*d - shibbit - O3 x4x4x x3x3x3*d - hitosbit - O42 s4s4s x3o3o3*d - tasist - O37 s4s4s x3x3o3*d - thisosbit - O61 s4s4s x3x3x3*d - hisosbit - O46 ``` ```x3o3o3*a x3o3o3*d - tribbit - O29 x3o3o3*a x3x3o3*d - tathibbit - O32 x3x3o3*a x3x3o3*d - thabbit - O56 x3o3o3*a x3x3x3*d - thibbit - O30 x3x3o3*a x3x3x3*d - hithibbit - O41 x3x3x3*a x3x3x3*d - hibbit - O39 ``` ```x∞o x∞o x3o6o - tisbat - O2 x∞o x∞o o3x6o - thisbit - O5 x∞o x∞o o3o6x - shibbit - O3 x∞x x∞o x3o6o - tisbat - O2 x∞x x∞o o3x6o - thisbit - O5 x∞x x∞o o3o6x - shibbit - O3 x∞o x∞o x3x6o - shibbit - O3 x∞o x∞o x3o6x - rithsibbit - O8 x∞o x∞o o3x6x - thosbit - O7 x∞x x∞x x3o6o - tisbat - O2 x∞x x∞x o3x6o - thisbit - O5 x∞x x∞x o3o6x - shibbit - O3 x∞x x∞o x3x6o - shibbit - O3 x∞x x∞o x3o6x - rithsibbit - O8 x∞x x∞o o3x6x - thosbit - O7 x∞o x∞o x3x6x - otathisbit - O9 x∞x x∞x x3x6o - shibbit - O3 x∞x x∞x x3o6x - rithsibbit - O8 x∞x x∞x o3x6x - thosbit - O7 x∞x x∞o x3x6x - otathisbit - O9 x∞x x∞x x3x6x - otathisbit - O9 x∞o x∞o s3s6s - sithsobit - O11 ``` ```x∞o x∞o x4o4o - test - O1 x∞o x∞o o4x4o - test - O1 x∞x x∞o x4o4o - test - O1 x∞x x∞o o4x4o - test - O1 x∞o x∞o x4x4o - tososbit - O6 x∞o x∞o x4o4x - test - O1 x∞x x∞x x4o4o - test - O1 x∞x x∞x o4x4o - test - O1 x∞x x∞o x4x4o - tososbit - O6 x∞x x∞o x4o4x - test - O1 x∞o x∞o x4x4x - tososbit - O6 x∞x x∞x x4x4o - tososbit - O6 x∞x x∞x x4o4x - test - O1 x∞x x∞o x4x4x - tososbit - O6 x∞x x∞x x4x4x - tososbit - O6 x∞o x∞o s4s4s - sisosbit - O10 ``` o∞o o∞o o3o3o3*e = A1×A1×A2 = W(2)2×P(3) o∞o o∞o o∞o o∞o = A1×A1×A1×A1 = W(2)4 other uniforms ```x∞o x∞o x3o3o3*e - tisbat - O2 x∞x x∞o x3o3o3*e - tisbat - O2 x∞o x∞o x3x3o3*e - thisbit - O5 x∞x x∞x x3o3o3*e - tisbat - O2 x∞x x∞o x3x3o3*e - thisbit - O5 x∞o x∞o x3x3x3*e - shibbit - O3 x∞x x∞x x3x3o3*e - thisbit - O5 x∞x x∞o x3x3x3*e - shibbit - O3 x∞x x∞x x3x3x3*e - shibbit - O3 ``` ```x∞o x∞o x∞o x∞o - test - O1 x∞x x∞o x∞o x∞o - test - O1 x∞x x∞x x∞o x∞o - test - O1 x∞x x∞x x∞x x∞o - test - O1 x∞x x∞x x∞x x∞x - test - O1 ``` ```elong( x3o3o3o3o3*a ) - ecypit - O141 elongated cyclopentachoric TC, elongated pentachoric-dispentachoric TC schmo( x3o3o3o3o3*a ) - zucypit - O142 schmoozed cyclopentachoric TC, schmoozed pentachoric-dispentachoric TC elongschmo( x3o3o3o3o3*a ) - ezucypit - O143 elongated schmoozed cyclopentachoric TC, elongated schmoozed pentachoric-dispentachoric TC elong( x3o6o x3o6o ) - etbit - O31 elongated triangular duoprismatic TC elong( x3o6o o3x6o ) - etothbit - O49 elongated triangular-trihexagonal duoprismatic TC elong( x3o6o o3o6x ) - ethibit - O40 elongated triangular-hexagonal duoprismatic TC elong( x3o6o x3x6o ) - ethibit - O40 elong( x3o6o x3o6x ) - etrithit - O52 elongated triangular-rhombitrihexagonal TC elong( x3o6o o3x6x ) - etathobit - O51 elongated triangular-tomohexagonal duoprismatic TC elong( x3o6o x3x6x ) - etotithat - O53 elongated triangular-omnitruncated-trihexagonal TC elong( x3o6o s3s6s ) - etasithit - O55 elongated triangular-simotrihexagonal TC elong( elong( x3o6o x3o6o )) - betobit - O48 bielongated triangular duoprismatic TC elong( x3o6o elong( x3o6o )) - betobit - O48 x3o6o elong( x3o6o ) - etbit - O31 o3x6o elong( x3o6o ) - etothbit - O49 o3o6x elong( x3o6o ) - ethibit - O40 x3x6o elong( x3o6o ) - ethibit - O40 x3o6x elong( x3o6o ) - etrithit - O52 o3x6x elong( x3o6o ) - etathobit - O51 x3x6x elong( x3o6o ) - etotithat - O53 s3s6s elong( x3o6o ) - etasithit - O55 elong( x3o6o ) elong( x3o6o ) - betobit - O48 elong( x3o6o x4o4o ) - etsobit - O4 elongated triangular-square duoprismatic TC elong( x3o6o x4x4o ) - etatosbit - O50 elongated triangular-tomosquare duoprismatic TC elong( x3o6o x4x4x ) - etatosbit - O50 elong( x3o6o s4s4s ) - etasist - O54 elongated triangular-simosquare TC gyro( x3o6o x4o4o ) - gytosbit - O12 gyrated triangular-square duoprismatic TC gyroelong( x3o6o x4o4o ) - egytsobit - O13 elongated gyrated triangular-square duoprismatic TC bigyro( x3o6o x4o4o ) - bigytsbit - O84 bigyrated triangular-square duoprismatic TC bigyroelong( x3o6o x4o4o ) - ebiytsbit - O85 elongated bigyrated triangular-square duoprismatic TC prismatogyro( x3o6o x4o4o ) - pegytsbit - O86 prismatoelongated gyrated triangular-square duoprismatic TC gyro( elong( x3o6o ) x4o4o ) - egytsobit - O13 bigyro( elong( x3o6o ) x4o4o ) - ebiytsbit - O85 elong( x3o6o ) x4o4o - etsobit - O4 elong( x3o6o ) x4x4o - etatosbit - O50 elong( x3o6o ) x4x4x - etatosbit - O50 elong( x3o6o ) s4s4s - etasist - O54 elong( x3o6o x3o3o3*d ) - etbit - O31 elong( x3o6o x3x3o3*d ) - etothbit - O49 elong( x3o6o x3x3x3*d ) - ethibit - O40 elong( o3x6o x3o3o3*d ) - etothbit - O49 elong( o3o6x x3o3o3*d ) - ethibit - O40 elong( x3x6o x3o3o3*d ) - ethibit - O40 elong( x3o6x x3o3o3*d ) - etrithit - O52 elong( o3x6x x3o3o3*d ) - etathobit - O51 elong( x3x6x x3o3o3*d ) - etotithat - O53 elong (s3s6s x3o3o3*d ) - etasithit - O55 elong( elong( x3o6o x3o3o3*d )) - betobit - O48 elong( x3o6o elong( x3o3o3*d )) - betobit - O48 elong( elong( x3o6o ) x3o3o3*d ) - betobit - O48 x3o6o elong( x3o3o3*d ) - etbit - O31 o3x6o elong( x3o3o3*d ) - etothbit - O49 o3o6x elong( x3o3o3*d ) - ethibit - O40 x3x6o elong( x3o3o3*d ) - ethibit - O40 x3o6x elong( x3o3o3*d ) - etrithit - O52 o3x6x elong( x3o3o3*d ) - etathobit - O51 x3x6x elong( x3o3o3*d ) - etotithat - O53 s3s6s elong( x3o3o3*d ) - etasithit - O55 elong( x3o6o ) x3o3o3*d - etbit - O31 elong( x3o6o ) x3x3o3*d - etothbit - O49 elong( x3o6o ) x3x3x3*d - ethibit - O40 elong( x3o6o ) elong( x3o3o3*d ) - betobit - O48 elong( x3o3o3*a x4x4o ) - etatosbit - O50 elong( x3o3o3*a x4x4x ) - etatosbit - O50 elong( x3o3o3*a s4s4s ) - etasist - O54 gyro( x3o3o3*a x4o4o ) - gytosbit - O12 gyroelong( x3o3o3*a x4o4o ) - egytsobit - O13 bigyro( x3o3o3*a x4o4o ) - bigytsbit - O84 bigyroelong( x3o3o3*a x4o4o ) - ebiytsbit - O85 prismatogyro( x3o3o3*a x4o4o ) - pegytsbit - O86 gyro( elong( x3o3o3*a ) x4o4o ) - egytsobit - O13 bigyro( elong( x3o3o3*a ) x4o4o ) - ebiytsbit - O85 elong( x3o3o3*a ) x4x4o - etatosbit - O50 elong( x3o3o3*a ) x4x4x - etatosbit - O50 elong( x3o3o3*a ) s4s4s - etasist - O54 elong( x3o3o3*a x3o3o3*d ) - etbit - O31 elong( x3o3o3*a x3x3o3*d ) - etothbit - O49 elong( x3o3o3*a x3x3x3*d ) - ethibit - O40 elong( elong( x3o3o3*a x3o3o3*d )) - betobit - O48 elong( x3o3o3*a elong( x3o3o3*d )) - betobit - O48 x3o3o3*a elong( x3o3o3*d ) - etbit - O31 x3x3o3*a elong( x3o3o3*d ) - etothbit - O49 x3x3x3*a elong( x3o3o3*d ) - ethibit - O40 elong( x3o3o3*a ) elong( x3o3o3*d ) - betobit - O48 elong( x∞o x3o3o *d4o ) - eacpit - O23 elongated-alternated-cubic prismatic TC gyro( x∞o x3o3o *d4o ) - gyacpit - O22 gyrated-alternated-cubic prismatic TC gyroelong( x∞o x3o3o *d4o ) - gyeacpit - O24 gyrated-elongated-alternated-cubic prismatic TC x∞o elong( x3o3o *d4o ) - eacpit - O23 x∞o gyro( x3o3o *d4o ) - gyacpit - O22 x∞o gyroelong( x3o3o *d4o ) - gyeacpit - O24 elong( x∞o x3o3o3o3*c ) - eacpit - O23 gyro( x∞o x3o3o3o3*c ) - gyacpit - O22 gyroelong( x∞o x3o3o3o3*c ) - gyeacpit - O24 x∞o elong( x3o3o3o3*c ) - eacpit - O23 x∞o gyro( x3o3o3o3*c ) - gyacpit - O22 x∞o gyroelong( x3o3o3o3*c ) - gyeacpit - O24 gyro( x∞o x∞o x3o6o ) - gytosbit - O12 gyroelong( x∞o x∞o x3o6o ) - egytsobit - O13 bigyro( x∞o x∞o x3o6o ) - bigytsbit - O84 bigyroelong( x∞o x∞o x3o6o ) - ebiytsbit - O85 prismatogyro( x∞o x∞o x3o6o ) - pegytsbit - O86 elong( x∞o gyro( x∞o x3o6o )) - egytsobit - O13 gyro( x∞o gyro( x∞o o3x6o )) - bigytsbit - O84 gyroelong( x∞o gyro( x∞o o3x6o )) - ebiytsbit - O85 gyro( x∞o x∞o elong( x3o6o )) - egytsobit - O13 bigyro( x∞o x∞o elong( x3o6o )) - ebiytsbit - O85 x∞o elong( x∞o x3o6o ) - etsobit - O4 x∞o gyro( x∞o x3o6o ) - gytosbit - O12 x∞o gyroelong( x∞o x3o6o ) - egytsobit - O13 gyro( x∞o x∞o x3o3o3*e ) - gytosbit - O12 gyroelong( x∞o x∞o x3o3o3*e ) - egytsobit - O13 bigyro( x∞o x∞o x3o3o3*e ) - bigytsbit - O84 bigyroelong( x∞o x∞o x3o3o3*e ) - ebiytsbit - O85 prismatogyro( x∞o x∞o x3o3o3*e ) - pegytsbit - O86 elong( x∞o gyro( x∞o x3o3o3*e )) - egytsobit - O13 gyro( x∞o gyro( x∞o x3x3o3*e )) - bigytsbit - O84 gyroelong( x∞o gyro( x∞o x3x3o3*e )) - ebiytsbit - O85 gyro( x∞o x∞o elong( x3o3o3*e )) - egytsobit - O13 bigyro( x∞o x∞o elong( x3o3o3*e )) - ebiytsbit - O85 x∞o gyro( x∞o x3o3o3*e ) - gytosbit - O12 x∞o gyroelong( x∞o x3o3o3*e ) - egytsobit - O13 ... -schmo- = ...-0-0-... -gyro- = ...-0-1-0-1-... -bigyro- = ...-0-1-2-0-1-2-... -prismatogyro- = ...-0-1-0-2-0-1-0-2-... ```

In 4D too there are several different lattices.

In the pentachoric area there are 2 lattices, A4 and A4*. The latter of which can be considered as a superposition of 5 of the former, each having a 1/5 rotated Dynkin diagram. The Delone complex of A4 is cypit. The Voronoi complex of A4* is otcypit.

In the tesseractic area there is the primitive cubical one, C4. Its Voronoi complex and its Delone complex both are relatively shifted test.

Next there is the body-centered tesseractic (bct) lattice. Thus it is the union of the primitive cubical tesseractic plus its Voronoi cell vertices ("holes"). Alternatively this one can be described either as lattice B4, as lattice D4, or as lattice F4. The Voronoi complex here is icot. The Delone complex is hext.

```----
5D  Pentacombs (up)
----
```

So far just the quasiregular ones of the irreducible groups.

 o4o3o3o3o4o = C5 = R(6) o3o3o *b3o3o4o = B5 = S(6) o3o3o o3o3o *b3*e = D5 = Q(6) o3o3o3o3o3o3*a = A5 = P(6) ```x4o3o3o3o4o - penth o4x3o3o3o4o - rinoh o4o3x3o3o4o - brinoh ``` ```x3o3o *b3o3o4o - hinoh o3x3o *b3o3o4o - brinoh o3o3o *b3x3o4o - brinoh o3o3o *b3o3x4o - rinoh o3o3o *b3o3o4x - penth ``` ```x3o3o o3o3o *b3*e - hinoh o3x3o o3o3o *b3*e - brinoh ``` ```x3o3o3o3o3o3*a - cyxh ```

```----
6D  Hexacombs (up)
----
```

So far just the quasiregular ones of the irreducible groups.

 o4o3o3o3o3o4o = C6 = R(7) o3o3o *b3o3o3o4o = B6 = S(7) o3o3o o3o3o *b3o3*e = D6 = Q(7) o3o3o3o3o3o3o3*a = A6 = P(7) o3o3o3o3o *c3o3o = E6 = T(7) ```x4o3o3o3o3o4o - o4x3o3o3o3o4o - o4o3x3o3o3o4o - o4o3o3x3o3o4o - ``` ```x3o3o *b3o3o3o4o - o3x3o *b3o3o3o4o - o3o3o *b3x3o3o4o - o3o3o *b3o3x3o4o - o3o3o *b3o3o3x4o - o3o3o *b3o3o3o4x - ``` ```x3o3o o3o3o *b3o3*e - o3x3o o3o3o *b3o3*e - o3o3o o3o3o *b3x3*e - ``` ```x3o3o3o3o3o3o3*a - ``` ```x3o3o3o3o *c3o3o - o3x3o3o3o *c3o3o - o3o3x3o3o *c3o3o - ```

```----
7D  Heptacombs (up)
----
```

Just the quasiregular ones of the irreducible groups.

 o4o3o3o3o3o3o4o = C7 = R(8) o3o3o *b3o3o3o3o4o = B7 = S(8) o3o3o o3o3o *b3o3o3*e = D7 = Q(8) o3o3o3o3o3o3o3o3*a = A7 = P(8) o3o3o3o3o3o3o *d3o = E7 = T(8) ```x4o3o3o3o3o3o4o - o4x3o3o3o3o3o4o - o4o3x3o3o3o3o4o - o4o3o3x3o3o3o4o - ``` ```x3o3o *b3o3o3o3o4o - o3x3o *b3o3o3o3o4o - o3o3o *b3x3o3o3o4o - o3o3o *b3o3x3o3o4o - o3o3o *b3o3o3x3o4o - o3o3o *b3o3o3o3x4o - o3o3o *b3o3o3o3o4x - ``` ```x3o3o o3o3o *b3o3o3*e - o3x3o o3o3o *b3o3o3*e - o3o3o o3o3o *b3x3o3*e - ``` ```x3o3o3o3o3o3o3o3*a - ``` ```x3o3o3o3o3o3o *d3o - o3x3o3o3o3o3o *d3o - o3o3x3o3o3o3o *d3o - o3o3o3x3o3o3o *d3o - o3o3o3o3o3o3o *d3x - ```

```----
8D  Octacombs (up)
----
```

Just the quasiregular ones of the irreducible groups.

 o4o3o3o3o3o3o3o4o = C8 = R(9) o3o3o *b3o3o3o3o3o4o = B8 = S(9) o3o3o o3o3o *b3o3o3o3*e = D8 = Q(9) o3o3o3o3o3o3o3o3o3*a = A8 = P(9) o3o3o3o3o3o3o3o *c3o = E8 = T(9) ```o4o3o3o3o3o3o3o4o - o4o3o3o3o3o3o3o4o - o4o3o3o3o3o3o3o4o - o4o3o3o3o3o3o3o4o - o4o3o3o3o3o3o3o4o - ``` ```x3o3o *b3o3o3o3o3o4o - o3x3o *b3o3o3o3o3o4o - o3o3o *b3x3o3o3o3o4o - o3o3o *b3o3x3o3o3o4o - o3o3o *b3o3o3x3o3o4o - o3o3o *b3o3o3o3x3o4o - o3o3o *b3o3o3o3o3x4o - o3o3o *b3o3o3o3o3o4x - ``` ```x3o3o o3o3o *b3o3o3o3*e - o3x3o o3o3o *b3o3o3o3*e - o3o3o o3o3o *b3x3o3o3*e - o3o3o o3o3o *b3o3x3o3*e - ``` ```x3o3o3o3o3o3o3o3o3*a - ``` ```x3o3o3o3o3o3o3o *c3o - o3x3o3o3o3o3o3o *c3o - o3o3x3o3o3o3o3o *c3o - o3o3o3x3o3o3o3o *c3o - o3o3o3o3x3o3o3o *c3o - o3o3o3o3o3x3o3o *c3o - o3o3o3o3o3o3x3o *c3o - o3o3o3o3o3o3o3x *c3o - o3o3o3o3o3o3o3o *c3x - ```