Editing Convex uniform honeycomb (section)

=== The C̃<sub>3</sub>, [4,3,4] group (cubic) ===
The regular cubic honeycomb, represented by Schläfli symbol {4,3,4}, offers seven unique derived uniform honeycombs via truncation operations. (One redundant form, the ''runcinated cubic honeycomb'', is included for completeness though identical to the cubic honeycomb.) The reflectional symmetry is the affine [[Coxeter group]] [4,3,4]. There are four index 2 subgroups that generate alternations: [1<sup>+</sup>,4,3,4], [(4,3,4,2<sup>+</sup>)], [4,3<sup>+</sup>,4], and [4,3,4]<sup>+</sup>, with the first two generated repeated forms, and the last two are nonuniform.

{{C3 honeycombs}}

{{Clear|right}}
{|class="wikitable" style="text-align:center;"
|+ [4,3,4], [[space group]] Pm{{overline|3}}m (221)
!rowspan=2|Reference<br/>Indices
!rowspan=2|Honeycomb name<br/>[[Coxeter diagram]]<br/>and [[Schläfli symbol#Extended for uniform 4-polytopes and 3-space honeycombs|Schläfli symbol]]
! colspan=6|Cell counts/vertex<br/>and positions in cubic honeycomb<br/>
!rowspan=2|Frames<br/>(Perspective)
!rowspan=2|[[Vertex figure]]
!rowspan=2|Dual cell
|- 
!(0)<br/>{{CDD|node|3|node|4|node}} 
!(1)<br/>{{CDD|node|2|node|4|node}} 
!(2)<br/>{{CDD|node|4|node|2|node}} 
!(3)<br/>{{CDD|node|4|node|3|node}}
!Alt
!Solids<br/>(Partial)
|- 
|J<sub>11,15</sub><br/>A<sub>1</sub><br/>W<sub>1</sub><br/>G<sub>22</sub><br/>&delta;<sub>4</sub>
|[[cubic honeycomb|cubic]] (chon)<br/>{{CDD|node_1|4|node|3|node|4|node}} <br/>t<sub>0</sub>{4,3,4}<br/>{4,3,4}
|&nbsp;
|&nbsp;
|&nbsp;
|(8)<br/>[[File:hexahedron.png|30px]]<br/>[[cube|(4.4.4)]]
|&nbsp;
| [[File:Partial cubic honeycomb.png|75px]]
|[[File:Cubic honeycomb.png|75px]]
|[[File:Cubic honeycomb verf.svg|75px]]<br/>[[octahedron]]
| [[File:Cubic full domain.png|80px]]<br/>[[Cube]], {{CDD|node_f1|3|node|4|node}}
|- 
|J<sub>12,32</sub><br/>A<sub>15</sub><br/>W<sub>14</sub><br/>G<sub>7</sub><br/>O<sub>1</sub>
|[[rectified cubic honeycomb|rectified cubic]] (rich)<br/>{{CDD|node|4|node_1|3|node|4|node}} <br/>t<sub>1</sub>{4,3,4}<br/>r{4,3,4}
|(2)<br/>[[File:octahedron.png|30px]]<br/>[[octahedron|(3.3.3.3)]]
|&nbsp;
|&nbsp;
|(4)<br/>[[File:cuboctahedron.png|30px]]<br/>[[cuboctahedron|(3.4.3.4)]]
|&nbsp;
|[[File:Rectified cubic honeycomb.png|75px]]
|[[File:Rectified cubic tiling.png|75px]]
|[[File:Rectified cubic honeycomb verf.png|75px]]<br/>[[cuboid]]
|[[File:Cubic square bipyramid.png|80px]]<BR/>[[Square bipyramid]]<BR/>{{CDD|node_f1|2|node_f1|4|node}}
|- 
|J<sub>13</sub><br/>A<sub>14</sub><br/>W<sub>15</sub><br/>G<sub>8</sub><br/>t<sub>1</sub>&delta;<sub>4</sub><br/>O<sub>15</sub>
|[[truncated cubic honeycomb|truncated cubic]] (tich)<br/>{{CDD|node_1|4|node_1|3|node|4|node}} <br/>t<sub>0,1</sub>{4,3,4}<br/>t{4,3,4}
|(1)<br/>[[File:octahedron.png|30px]]<br/>[[octahedron|(3.3.3.3)]]
|&nbsp;
|&nbsp;
|(4)<br/>[[File:truncated hexahedron.png|30px]]<br/>[[truncated cube|(3.8.8)]]
|&nbsp;
|[[File:Truncated cubic honeycomb.png|75px]]
|[[File:Truncated cubic tiling.png|75px]]
|[[File:Truncated cubic honeycomb verf.png|75px]]<br/>[[square pyramid]]
|[[File:Cubic square pyramid.png|80px]]<BR/>Isosceles [[square pyramid]]
|- 
|J<sub>14</sub><br/>A<sub>17</sub><br/>W<sub>12</sub><br/>G<sub>9</sub><br/>t<sub>0,2</sub>&delta;<sub>4</sub><br/>O<sub>14</sub>
|[[Cantellated cubic honeycomb|cantellated cubic]] (srich)<br/>{{CDD|node_1|4|node|3|node_1|4|node}} <br/>t<sub>0,2</sub>{4,3,4}<br/>rr{4,3,4}
|(1)<br/>[[File:cuboctahedron.png|30px]]<br/>[[cuboctahedron|(3.4.3.4)]]
|(2)<br/>[[File:hexahedron.png|30px]]<br/>[[cube|(4.4.4)]]
|&nbsp;
|(2)<br/>[[File:small rhombicuboctahedron.png|30px]]<br/>[[rhombicuboctahedron|(3.4.4.4)]]
|&nbsp;
|[[File:Cantellated cubic honeycomb.jpg|75px]]
|[[File:Cantellated cubic tiling.png|75px]]
|[[File:Cantellated cubic honeycomb verf.png|75px]]<br/>oblique [[triangular prism]]
|[[File:Quarter oblate octahedrille cell.png|80px]]<BR/>[[Triangular bipyramid]]
|- 
|J<sub>17</sub><br/>A<sub>18</sub><br/>W<sub>13</sub><br/>G<sub>25</sub><br/>t<sub>0,1,2</sub>&delta;<sub>4</sub><br/>O<sub>17</sub>
|[[cantitruncated cubic honeycomb|cantitruncated cubic]] (grich)<br/>{{CDD|node_1|4|node_1|3|node_1|4|node}} <br/>t<sub>0,1,2</sub>{4,3,4}<br/>tr{4,3,4}
|(1)<br/>[[File:truncated octahedron.png|30px]]<br/>[[truncated octahedron|(4.6.6)]]
|(1)<br/>[[File:hexahedron.png|30px]]<br/>[[cube|(4.4.4)]]
|&nbsp;
|(2)<br/>[[File:Great rhombicuboctahedron.png|30px]]<br/>[[Truncated cuboctahedron|(4.6.8)]]
|&nbsp;
|[[File:Cantitruncated Cubic Honeycomb.svg|75px]]
|[[File:Cantitruncated cubic tiling.png|75px]]
|[[File:Cantitruncated cubic honeycomb verf.png|75px]]<br/>irregular [[tetrahedron]]
|[[File:Triangular pyramidille cell1.png|80px]]<BR/>[[Triangular pyramidille]]
|- 
|J<sub>18</sub><br/>A<sub>19</sub><br/>W<sub>19</sub><br/>G<sub>20</sub><br/>t<sub>0,1,3</sub>&delta;<sub>4</sub><br/>O<sub>19</sub>
|[[runcitruncated cubic honeycomb|runcitruncated cubic]] (prich)<br/>{{CDD|node_1|4|node_1|3|node|4|node_1}}<br/>t<sub>0,1,3</sub>{4,3,4}
|(1)<br/>[[File:small rhombicuboctahedron.png|30px]]<br/>[[rhombicuboctahedron|(3.4.4.4)]]
|(1)<br/>[[File:hexahedron.png|30px]]<br/>[[cube|(4.4.4)]]
|(2)<br/>[[File:octagonal prism.png|30px]]<br/>[[octagonal prism|(4.4.8)]]
|(1)<br/>[[File:truncated hexahedron.png|30px]]<br/>[[truncated cube|(3.8.8)]]
|&nbsp;
|[[File:Runcitruncated cubic honeycomb.jpg|75px]]
|[[File:Runcitruncated cubic tiling.png|75px]]
|[[File:Runcitruncated cubic honeycomb verf.png|75px]]<br/>oblique trapezoidal pyramid
|[[File:Square quarter pyramidille cell.png|80px]] <BR/>[[Square quarter pyramidille]] 
|- valign=top BGCOLOR="#d0f0f0"
|J<sub>21,31,51</sub><br/>A<sub>2</sub><br/>W<sub>9</sub><br/>G<sub>1</sub><br/>h&delta;<sub>4</sub><br/>O<sub>21</sub>
|[[Tetrahedral-octahedral honeycomb|alternated cubic]] (octet)<br/>{{CDD|node_h1|4|node|3|node|4|node}}<br/>h{4,3,4}
|&nbsp;
|&nbsp;
|&nbsp;
|(8)<br/>[[File:Tetrahedron.png|30px]]<br/>[[Tetrahedron|(3.3.3)]]
|(6)<br/>[[File:Octahedron.png|30px]]<br/>[[Octahedron|(3.3.3.3)]]
|[[File:Tetrahedral-octahedral honeycomb.png|76px]]
|[[File:Alternated cubic tiling.png|75px]]
|[[File:Alternated cubic honeycomb verf.svg|75px]]<br/>[[cuboctahedron]]
|[[File:Dodecahedrille cell.png|80px]]<BR/>[[Dodecahedrille]]
|- valign=top BGCOLOR="#d0f0f0"
|J<sub>22,34</sub><br/>A<sub>21</sub><br/>W<sub>17</sub><br/>G<sub>10</sub><br/>h<sub>2</sub>&delta;<sub>4</sub><br/>O<sub>25</sub>
|[[Cantic cubic honeycomb|Cantic cubic]] (tatoh)<br/>{{CDD|node_h1|4|node|3|node_1|4|node}} ↔ {{CDD|nodes_10ru|split2|node_1|4|node}}
|(1)<br/>[[File:Cuboctahedron.png|30px]][[cuboctahedron|(3.4.3.4)]]
|&nbsp;
|
|(2)<br/>[[File:Truncated tetrahedron.png|30px]][[Truncated tetrahedron|(3.6.6)]]
|(2)<br/>[[File:Truncated octahedron.png|30px]][[truncated octahedron|(4.6.6)]]
|[[File:Truncated Alternated Cubic Honeycomb.svg|75px]]
|[[File:Truncated alternated cubic tiling.png|75px]]
|[[File:Truncated alternated cubic honeycomb verf.png|60px]]<br/>rectangular pyramid
|[[File:Half oblate octahedrille cell.png|80px]]<BR/>[[Half oblate octahedrille]]
|- valign=top BGCOLOR="#d0f0f0"
|J<sub>23</sub><br/>A<sub>16</sub><br/>W<sub>11</sub><br/>G<sub>5</sub><br/>h<sub>3</sub>&delta;<sub>4</sub><br/>O<sub>26</sub>
|[[Runcic cubic honeycomb|Runcic cubic]] (sratoh)<br/>{{CDD|node_h1|4|node|3|node|4|node_1}} ↔ {{CDD|nodes_10ru|split2|node|4|node_1}}
|(1)<br>[[File:hexahedron.png|30px]]<br/>[[cube|(4.4.4)]]
|&nbsp;
|
|(1)<br>[[File:tetrahedron.png|30px]]<br/>[[tetrahedron|(3.3.3)]]
|(3)<br>[[File:small rhombicuboctahedron.png|30px]]<br/>[[rhombicuboctahedron|(3.4.4.4)]]
|[[File:Runcinated alternated cubic honeycomb.jpg|75px]]
|[[File:Runcinated alternated cubic tiling.png|75px]]
|[[File:Runcinated alternated cubic honeycomb verf.png|60px]]<br/>tapered [[triangular prism]]
|[[File:Quarter cubille cell.png|80px]]<BR/>[[Quarter cubille]]
|- valign=top BGCOLOR="#d0f0f0"
|J<sub>24</sub><br/>A<sub>20</sub><br/>W<sub>16</sub><br/>G<sub>21</sub><br/>h<sub>2,3</sub>&delta;<sub>4</sub><br/>O<sub>28</sub>
|[[Runcicantic cubic honeycomb|Runcicantic cubic]] (gratoh)<br/>{{CDD|node_h1|4|node|3|node_1|4|node_1}} ↔ {{CDD|nodes_10ru|split2|node_1|4|node_1}}
|(1)<br>[[File:truncated hexahedron.png|30px]]<br/>[[truncated cube|(3.8.8)]]
|&nbsp;
|
|(1)<br>[[File:truncated tetrahedron.png|30px]]<br/>[[truncated tetrahedron|(3.6.6)]]
|(2)<br>[[File:Great rhombicuboctahedron.png|30px]]<br/>[[truncated cuboctahedron|(4.6.8)]]
|[[File:Cantitruncated alternated cubic honeycomb.png|75px]]
|[[File:Cantitruncated alternated cubic tiling.png|75px]]
|[[File:Runcitruncated alternate cubic honeycomb verf.png|60px]]<br/>Irregular [[tetrahedron]]
|[[File:Half pyramidille cell.png|80px]]<BR/>[[Half pyramidille]]
|- valign=top BGCOLOR="#d0f0f0"
|Nonuniform<sub>b</sub>
|[[snub rectified cubic honeycomb|snub rectified cubic]] (serch)<br/>{{CDD|node_h|4|node_h|3|node_h|4|node}}<br/>sr{4,3,4}
|(1)<br>[[File:Uniform polyhedron-43-h01.svg|30px]]<br/>[[Regular icosahedron|(3.3.3.3.3)]]<br/>{{CDD|node_h|3|node_h|4|node}}
|(1)<br>[[File:tetrahedron.png|30px]]<br/>[[tetrahedron|(3.3.3)]]<br/>{{CDD|node_h|2|node_h|4|node}}
|&nbsp;
|(2)<br>[[File:snub hexahedron.png|30px]]<br/>[[snub cube|(3.3.3.3.4)]]<br/>{{CDD|node_h|4|node_h|3|node_h}}
|(4)<br>[[File:tetrahedron.png|30px]]<br/>[[tetrahedron|(3.3.3)]]
|[[File:Alternated cantitruncated cubic honeycomb.png|75px]]
|
||[[File:Alternated cantitruncated cubic honeycomb verf.png|75px]]<br/>Irr. [[tridiminished icosahedron]]

|- valign=top BGCOLOR="#d0f0f0"
|Nonuniform
|[[Cantic snub cubic honeycomb|Cantic snub cubic]] (casch)<br/>{{CDD|node_1|4|node_h|3|node_h|4|node}}<br/>2s<sub>0</sub>{4,3,4}
|(1)<br>[[File:Uniform polyhedron-43-h01.svg|30px]]<br/>[[icosahedron#snub octahedron|(3.3.3.3.3)]]<br/>{{CDD|node_h|3|node_h|4|node}}
|
|
|(2)<br>[[File:Rhombicuboctahedron uniform edge coloring.png|30px]]<br/>[[rhombicuboctahedron|(3.4.4.4)]]<br/>{{CDD|node_h|3|node_h|4|node_1}}
|(3)<br>[[File:Triangular prism.png|30px]]<br>[[triangular prism|(3.4.4)]]
|
|
|
|- valign=top BGCOLOR="#d0f0f0"
|Nonuniform
|Runcicantic snub cubic (rusch)<br/>{{CDD|node_h|4|node_1|3|node|4|node_h}}
|(1)<br>[[File:Cuboctahedron.png|30px]]<br>[[cuboctahedron|(3.4.3.4)]]
|(2)<br>[[File:Cube rotorotational symmetry.png|30px]]<br>[[cube|(4.4.4)]]
|(1)<br>[[File:Tetrahedron.png|30px]]<br>[[tetrahedron|(3.3.3)]]
|(1)<br>[[File:Truncated tetrahedron.png|30px]]<br>[[truncated tetrahedron|(3.6.6)]]
|(3)<br>[[File:Triangular cupola.png|30px]]<br>[[triangular cupola|Tricup]]
|
|
|
|- valign=top BGCOLOR="#d0f0f0"
|Nonuniform
|[[Runcic cantitruncated cubic honeycomb|Runcic cantitruncated cubic]] (esch)<br/>{{CDD|node_h|4|node_h|3|node_h|4|node_1}} <br/>sr<sub>3</sub>{4,3,4}
|(1)<br>[[File:snub hexahedron.png|30px]]<br/>[[snub cube|(3.3.3.3.4)]]<br/>{{CDD|node_h|4|node_h|3|node_h}}
|(1)<br>[[File:Tetragonal prism.png|30px]]<br/>(4.4.4)<br/>{{CDD|node_h|4|node_h|2|node_1}}
|(1)<br>[[File:Cube rotorotational symmetry.png|30px]]<br/>[[cube|(4.4.4)]]<br/>{{CDD|node_h|2|node_h|4|node_1}}
|(1)<br>[[File:Rhombicuboctahedron uniform edge coloring.png|30px]]<br/>[[rhombicuboctahedron|(3.4.4.4)]]<br/>{{CDD|node_h|3|node_h|4|node_1}}
|(3)<br>[[File:Triangular prism.png|30px]]<br>[[triangular prism|(3.4.4)]]
|
|
|
|}

{|class="wikitable"
|+ {{brackets|4,3,4}} honeycombs, [[space group]] Im{{overline|3}}m (229)
|-
!rowspan=2|Reference<br/>Indices
!rowspan=2|Honeycomb name<br/>[[Coxeter diagram]]<br/>{{CDD|branch_c1|4a4b|nodeab_c2}}<br/>and [[Schläfli symbol#Extended for uniform 4-polytopes and 3-space honeycombs|Schläfli symbol]]
!colspan=3|Cell counts/vertex<br/>and positions in cubic honeycomb<br/>
!rowspan=2|Solids<br/>(Partial)
!rowspan=2|Frames<br/>(Perspective)
!rowspan=2|[[Vertex figure]]
!rowspan=2|Dual cell
|- 
!(0,3)<br/>{{CDD|node|3|node|4|node}}<br/>{{CDD|node|4|node|3|node}}
!(1,2)<br/>{{CDD|node|2|node|4|node}}<br/>{{CDD|node|4|node|2|node}}
!Alt
|- BGCOLOR="#e0f0e0"
|J<sub>11,15</sub><br/>A<sub>1</sub><br/>W<sub>1</sub><br/>G<sub>22</sub><br/>&delta;<sub>4</sub><br/>O<sub>1</sub>
|'''[[Runcination (geometry)|runcinated]] cubic'''<br/>(same as regular [[cubic honeycomb|cubic]]) (chon)<br/>{{CDD|branch|4a4b|nodes_11}}<br/>t<sub>0,3</sub>{4,3,4}
|(2)<br/>[[File:hexahedron.png|30px]]<br/>[[cube|(4.4.4)]]
|(6)<br/>[[File:hexahedron.png|30px]]<br/>[[cube|(4.4.4)]]
|&nbsp;
| [[File:Runcinated cubic honeycomb.png|75px]]
|[[File:Cubic honeycomb.png|75px]]
|[[File:Runcinated cubic honeycomb verf.png|75px]]<br/>[[octahedron]]
| [[File:Cubic full domain.png|80px]]<br/>[[Cube]]
|- valign=top BGCOLOR="#e0f0e0"
|J<sub>16</sub><br/>A<sub>3</sub><br/>W<sub>2</sub><br/>G<sub>28</sub><br/>t<sub>1,2</sub>&delta;<sub>4</sub><br/>O<sub>16</sub>
|[[Bitruncated cubic honeycomb|bitruncated cubic]] (batch)<br/>{{CDD|branch_11|4a4b|nodes}} <br/>t<sub>1,2</sub>{4,3,4}<br/>2t{4,3,4}
|(4)<br/>[[File:truncated octahedron.png|30px]]<br/>[[truncated octahedron|(4.6.6)]]
|&nbsp;
|&nbsp;
|[[File:Bitruncated cubic honeycomb.png|75px]]
|[[File:Bitruncated cubic tiling.png|75px]]
|[[File:Bitruncated cubic honeycomb verf.png|75px]]<br/>([[disphenoid]])
|[[File:Oblate tetrahedrille cell.png|80px]]<BR/>[[Oblate tetrahedrille]]
|- valign=top BGCOLOR="#e0f0e0"
|J<sub>19</sub><br/>A<sub>22</sub><br/>W<sub>18</sub><br/>G<sub>27</sub><br/>t<sub>0,1,2,3</sub>&delta;<sub>4</sub><br/>O<sub>20</sub>
|[[omnitruncated cubic honeycomb|omnitruncated cubic]] (gippich)<br/>{{CDD|branch_11|4a4b|nodes_11}}<br/>t<sub>0,1,2,3</sub>{4,3,4}
|(2)<br/>[[File:Great rhombicuboctahedron.png|30px]]<br/>[[Truncated cuboctahedron|(4.6.8)]]
|(2)<br/>[[File:octagonal prism.png|30px]]<br/>[[octagonal prism|(4.4.8)]]
|&nbsp;
|[[File:Omnitruncated cubic honeycomb.jpg|75px]]
|[[File:Omnitruncated cubic tiling.png|75px]]
|[[File:Omnitruncated cubic honeycomb verf.png|75px]]<br/>irregular [[tetrahedron]]
|[[File:Fundamental tetrahedron1.png|80px]]<BR/>[[Eighth pyramidille]]
|- valign=top BGCOLOR="#d0f0f0"
|J<sub>21,31,51</sub><br/>A<sub>2</sub><br/>W<sub>9</sub><br/>G<sub>1</sub><br/>h&delta;<sub>4</sub><br/>O<sub>27</sub>
|[[Quarter cubic honeycomb]] (cytatoh)<br/>{{CDD|branch|4a4b|nodes_h1h1}}<br/>ht<sub>0</sub>ht<sub>3</sub>{4,3,4}
|(2)<br/>[[File:Uniform polyhedron-33-t0.png|30px]]<br/>[[tetrahedron|(3.3.3)]]
|(6)<br/>[[File:Uniform polyhedron-33-t01.png|30px]]<br/>[[truncated tetrahedron|(3.6.6)]]
|
|[[File:quarter cubic honeycomb2.png|76px]]
|[[File:Bitruncated alternated cubic tiling.png|75px]]
|[[File:T01 quarter cubic honeycomb verf2.png|75px]]<br/>elongated [[triangular antiprism]]

|[[File:Oblate cubille cell.png|80px]]<BR/>[[Oblate cubille]]
|- valign=top BGCOLOR="#d0f0f0"
|J<sub>21,31,51</sub><br/>A<sub>2</sub><br/>W<sub>9</sub><br/>G<sub>1</sub><br/>h&delta;<sub>4</sub><br/>O<sub>21</sub>
|[[Alternated cubic honeycomb|Alternated runcinated cubic]] (octet)<br/>(same as alternated cubic)<br/>{{CDD|branch|4a4b|nodes_hh}}<br/>ht<sub>0,3</sub>{4,3,4}
|(2)<br/>[[File:Uniform polyhedron-33-t0.png|30px]]<br/>[[tetrahedron|(3.3.3)]]
|(6)<br/>[[File:Uniform polyhedron-33-t2.png|30px]]<br/>[[tetrahedron|(3.3.3)]]
|(6)<br/>[[File:Uniform polyhedron-33-t1.svg|30px]]<br/>[[octahedron|(3.3.3.3)]]
|[[File:Tetrahedral-octahedral honeycomb2.png|76px]]
|[[File:Alternated cubic tiling.png|75px]]
|[[File:Alternated cubic honeycomb verf.svg|75px]]<br/>[[cuboctahedron]]

|- valign=top BGCOLOR="#d0f0f0"
|Nonuniform
|[[Cubic honeycomb#Biorthosnub cubic honeycomb|Biorthosnub cubic honeycomb]] (gabreth)<br>{{CDD|branch_11|4a4b|nodes_hh}}<br/>2s<sub>0,3</sub>{(4,2,4,3)}
|(2)<br>[[File:Truncated octahedron.png|30px]]<br>[[truncated octahedron|(4.6.6)]]
|(2)<br>[[File:Cube rotorotational symmetry.png|30px]]<br/>[[cube|(4.4.4)]]
|(2)<br>[[File:Cantic snub hexagonal hosohedron2.png|30px]]<br/>[[hexagonal prism|(4.4.6)]]
|
|
|
|- valign=top BGCOLOR="#d0f0f0"
|Nonuniform<sub>a</sub>
|[[Bitruncated cubic honeycomb#Related polyhedra and honeycombs|Alternated bitruncated cubic]] (bisch)<br/>{{CDD|branch_hh|4a4b|nodes}}<br/>h2t{4,3,4}
|[[File:Uniform polyhedron-43-h01.svg|30px]] (4)<br/>[[Regular icosahedron|(3.3.3.3.3)]]
|&nbsp;
|[[File:tetrahedron.png|30px]] (4)<br/>[[tetrahedron|(3.3.3)]]
|[[File:Alternated bitruncated cubic honeycomb2.png|75px]]
|
||[[File:Alternated bitruncated cubic honeycomb verf.png|75px]]
|[[File:Ten-of-diamonds_decahedron_in_cube.png|80px]]
|- valign=top BGCOLOR="#d0f0f0"
|Nonuniform
|Cantic bisnub cubic (cabisch)<br>{{CDD|branch_hh|4a4b|nodes_11}}<br/>2s<sub>0,3</sub>{4,3,4}
|(2)<br>[[File:Rhombicuboctahedron uniform edge coloring.png|30px]]<br/>[[rhombicuboctahedron|(3.4.4.4)]]
|(2)<br>[[File:Tetragonal prism.png|30px]]<br/>(4.4.4)
|(2)<br>[[File:Cube rotorotational symmetry.png|30px]]<br/>[[cube|(4.4.4)]]
|
|
|
|- valign=top BGCOLOR="#d0f0f0"
|Nonuniform<sub>c</sub>
|[[Omnitruncated cubic honeycomb#Alternated omnitruncated cubic honeycomb|Alternated omnitruncated cubic]] (snich)<br/>{{CDD|branch_hh|4a4b|nodes_hh}}<br/>ht<sub>0,1,2,3</sub>{4,3,4}
|(2)<br>[[File:Snub hexahedron.png|30px]]<br/>[[Snub cube|(3.3.3.3.4)]]
|(2)<br>[[File:square antiprism.png|30px]]<br/>[[square antiprism|(3.3.3.4)]]
|(4)<br>[[File:tetrahedron.png|30px]]<br/>[[tetrahedron|(3.3.3)]]
|&nbsp;
|
||[[File:Snub cubic honeycomb verf.png|75px]]
|}