Editing Convex uniform honeycomb (section)

== Scaliform honeycomb==
A '''[[scaliform polytope|scaliform]] honeycomb''' is [[vertex-transitive]], like a ''uniform honeycomb'', with regular polygon faces while cells and higher elements are only required to be ''orbiforms'', equilateral, with their vertices lying on hyperspheres. For 3D honeycombs, this allows a subset of [[Johnson solid]]s along with the uniform polyhedra. Some scaliforms can be generated by an alternation process, leaving, for example, [[pyramid (geometry)|pyramid]] and [[cupola (geometry)|cupola]] gaps.<ref>{{Cite web|url=http://bendwavy.org/klitzing/explain/polytope-tree.htm#scaliform|title = Polytope-tree}}</ref>

{| class=wikitable style="text-align:center; width:600px;"
|+ Euclidean honeycomb scaliforms
!colspan=3|Frieze slabs
!Prismatic stacks
|-
!s<sub>3</sub>{2,6,3}, {{CDD|node_h|2x|node_h|6|node|3|node_1}}
!s<sub>3</sub>{2,4,4}, {{CDD|node_h|2x|node_h|4|node|4|node_1}}
!s{2,4,4}, {{CDD|node_h|2x|node_h|4|node|4|node}}
!3s<sub>4</sub>{4,4,2,&infin;}, {{CDD|node|4|node|4|node_h|2x|node_h|infin|node_1}}
|-
|[[File:Runcic snub 263 honeycomb.png|200px]]
|[[File:Runcic snub 244 honeycomb.png|200px]]
|[[File:Alternated cubic slab honeycomb.png|200px]]
|[[File:Elongated square antiprismatic celluation.png|200px]]
|-
! [[File:triangular cupola.png|40px]] [[File:octahedron.png|40px]] [[File:Uniform polyhedron-63-t1-1.svg|40px]]
! [[File:square cupola.png|40px]] [[File:tetrahedron.png|40px]] [[File:Uniform tiling 44-t01.png|40px]]
! [[File:square pyramid.png|40px]] [[File:tetrahedron.png|40px]] [[File:Uniform tiling 44-t0.svg|40px]]
! [[File:square pyramid.png|40px]] [[File:tetrahedron.png|40px]] [[File:hexahedron.png|40px]]
|- valign=top
|[[File:s2s6o3x vertex figure.png|200px]]<br/>(1) 3.4.3.4: [[triangular cupola]]<br/>(2) 3.4.6: triangular cupola<br/>(1) 3.3.3.3: [[octahedron]]<br/>(1) 3.6.3.6: [[trihexagonal tiling]]
|[[File:s2s4o4x vertex figure.png|200px]]<br/>(1) 3.4.4.4: [[square cupola]]<br/>(2) 3.4.8: square cupola<br/>(1) 3.3.3: [[tetrahedron]]<br/>(1) 4.8.8: [[truncated square tiling]]
|[[File:O4o4s2s vertex figure.png|200px]]<br/>(1) 3.3.3.3: [[square pyramid]]<br/>(4) 3.3.4: square pyramid<br/>(4) 3.3.3: tetrahedron<br/>(1) 4.4.4.4: [[square tiling]]
|[[File:O4o4s2six vertex figure.png|200px]]<br/>(1) 3.3.3.3: square pyramid<br/>(4) 3.3.4: square pyramid<br/>(4) 3.3.3: tetrahedron<br/>(4) 4.4.4: [[cube]]
|}