Editing Convex uniform honeycomb (section)

=== Enumeration of Wythoff forms ===
All nonprismatic [[Wythoff construction]]s by Coxeter groups are given below, along with their [[alternation (geometry)|alternations]]. Uniform solutions are indexed with [[Branko Grünbaum]]'s listing. Green backgrounds are shown on repeated honeycombs, with the relations are expressed in the extended symmetry diagrams.
{| class=wikitable style="text-align:center;"
!Coxeter group
![[Goursat tetrahedron#Euclidean .28affine.29 3-space solutions|Extended<br/>symmetry]]
!colspan=2|Honeycombs
!Chiral<br/>extended<br/>symmetry
!colspan=2|Alternation honeycombs

|- 
|rowspan=4|[4,3,4]<br/>{{CDD|node|4|node|3|node|4|node}}||[4,3,4]<br/>{{CDD|node_c1|4|node_c2|3|node_c3|4|node_c4}}||6
| {{CDD|node_1|4|node|3|node|4|node}}<sub>22</sub> | {{CDD|node|4|node_1|3|node|4|node}}<sub>7</sub> | {{CDD|node_1|4|node_1|3|node|4|node}}<sub>8</sub><br/>{{CDD|node_1|4|node|3|node_1|4|node}}<sub>9</sub> | {{CDD|node_1|4|node_1|3|node_1|4|node}}<sub>25</sub> | {{CDD|node_1|4|node_1|3|node|4|node_1}}<sub>20</sub>
|[1<sup>+</sup>,4,3<sup>+</sup>,4,1<sup>+</sup>]||(2)
|{{CDD|node_h1|4|node|3|node|4|node}}<sub>1</sub> | {{CDD|node_h|4|node_h|3|node_h|4|node}}<sub>b</sub>
|- BGCOLOR="#e0f0e0"
|[2<sup>+</sup>[4,3,4]]<br/>{{CDD|node_c1|4|node|3|node|4|node_c1}} = {{CDD|node_c1|4|node|3|node|4|node}}||(1)
|{{CDD|node_1|4|node|3|node|4|node_1}} <sub>22</sub>
|[2<sup>+</sup>[(4,3<sup>+</sup>,4,2<sup>+</sup>)]]||(1)
|{{CDD|branch|4a4b|branch_hh|label2}}<sub>1</sub> | {{CDD|branch|4a4b|nodes_hh}}<sub>6</sub>

|- 
|[2<sup>+</sup>[4,3,4]]<br/>{{CDD|node_c1|4|node_c2|3|node_c2|4|node_c1}}||1
|{{CDD|node|4|node_1|3|node_1|4|node}}<sub>28</sub>
|[2<sup>+</sup>[(4,3<sup>+</sup>,4,2<sup>+</sup>)]]||(1)
|{{CDD|node|4|node_h|3|node_h|4|node}}<sub>a</sub>

|- 
|[2<sup>+</sup>[4,3,4]]<br/>{{CDD|node_c1|4|node_c2|3|node_c2|4|node_c1}}||2
|{{CDD|node_1|4|node_1|3|node_1|4|node_1}}<sub>27</sub>

|[2<sup>+</sup>[4,3,4]]<sup>+</sup>||(1)
|{{CDD|node_h|4|node_h|3|node_h|4|node_h}}<sub>c</sub>

|- 
|rowspan=3|[4,3<sup>1,1</sup>]<br/>{{CDD|node|4|node|split1|nodes}} ||[4,3<sup>1,1</sup>]<br/>{{CDD|node_c3|4|node_c4|split1|nodeab_c1-2}}||4
|{{CDD|node|4|node|split1|nodes_10lu}}<sub>1</sub> | {{CDD|node_1|4|node|split1|nodes_10lu}}<sub>7</sub> | {{CDD|node|4|node_1|split1|nodes_10lu}}<sub>10</sub> | {{CDD|node_1|4|node_1|split1|nodes_10lu}}<sub>28</sub>
|colspan=3|
|- BGCOLOR="#e0f0e0" align=center
|rowspan=2|[1[4,3<sup>1,1</sup>]]=[4,3,4]<br/>{{CDD|node_c1|4|node_c2|split1|nodeab_c3}} = {{CDD|node_c1|4|node_c2|3|node_c3|4|node_h0}}||rowspan=2|(7)
|rowspan=2|{{CDD|node_1|4|node|split1|nodes}}<sub>22</sub> | {{CDD|node|4|node_1|split1|nodes}}<sub>7</sub> | {{CDD|node_1|4|node_1|split1|nodes}}<sub>22</sub> | {{CDD|node|4|node|split1|nodes_11}}<sub>7</sub> | {{CDD|node_1|4|node|split1|nodes_11}}<sub>9</sub> | {{CDD|node|4|node_1|split1|nodes_11}}<sub>28</sub> | {{CDD|node_1|4|node_1|split1|nodes_11}}<sub>25</sub> 
|[1[1<sup>+</sup>,4,3<sup>1,1</sup>]]<sup>+</sup>||(2)
|{{CDD|node_h1|4|node|split1|nodes}}<sub>1</sub> | {{CDD|node_h1|4|node|split1|nodes_10lu}}<sub>6</sub> | {{CDD|node|4|node_h|split1|nodes_hh}}<sub>a</sub>
|- BGCOLOR="#e0f0e0" align=center
|[1[4,3<sup>1,1</sup>]]<sup>+</sup><br/>=[4,3,4]<sup>+</sup>||(1)
|{{CDD|node_h|4|node_h|split1|nodes_hh}}<sub>b</sub>

|- 
|rowspan=5|[3<sup>[4]</sup>]<br/>{{CDD|branch|3ab|branch}}||[3<sup>[4]</sup>]
|colspan=5|(none)
|- 
||[2<sup>+</sup>[3<sup>[4]</sup>]]<br/>{{CDD|branch_c1|3ab|branch_c2}} || 1
| {{CDD|branch_11|3ab|branch}}<sub>6</sub>
|colspan=3|
|- BGCOLOR="#e0f0e0" align=center
||[1[3<sup>[4]</sup>]]=[4,3<sup>1,1</sup>]<br/>{{CDD|node_c3|split1|nodeab_c1-2|split2|node_c3}} = {{CDD|node_h0|3|node_c3|split1|nodeab_c1-2}} || (2)
|{{CDD|node_1|split1|nodes|split2|node}}<sub>1</sub> | {{CDD|node_1|split1|nodes_11|split2|node}}<sub>10</sub>
|colspan=3|
|- BGCOLOR="#e0f0e0"
||[2[3<sup>[4]</sup>]]=[4,3,4]<br/>{{CDD|node_c1|split1|nodeab_c2|split2|node_c1}} = {{CDD|node_h0|4|node_c1|3|node_c2|4|node_h0}} || (1)
| {{CDD|node_1|split1|nodes|split2|node_1}}<sub>7</sub>
|colspan=3|
|- BGCOLOR="#e0f0e0" align=center
|[(2<sup>+</sup>,4)[3<sup>[4]</sup>]]=[2<sup>+</sup>[4,3,4]]<br/>{{CDD|branch_c1|3ab|branch_c1}} = {{CDD|node_h0|4|node_c1|3|node_c1|4|node_h0}} ||(1)
| {{CDD|branch_11|3ab|branch_11}}<sub>28</sub>
|[(2<sup>+</sup>,4)[3<sup>[4]</sup>]]<sup>+</sup><br/>= [2<sup>+</sup>[4,3,4]]<sup>+</sup>
|(1)|| {{CDD|branch_hh|3ab|branch_hh}}<sub>a</sub>

|}