Editing Convex uniform honeycomb (section)

=== Nonwythoffian forms (gyrated and elongated) ===
Three more uniform honeycombs are generated by breaking one or another of the above honeycombs where its faces form a continuous plane, then rotating alternate layers by 60 or 90 degrees (''gyration'') and/or inserting a layer of prisms (''elongation'').

The elongated and gyroelongated alternated cubic tilings have the same vertex figure, but are not alike. In the ''elongated'' form, each prism meets a tetrahedron at one triangular end and an octahedron at the other. In the ''gyroelongated'' form, prisms that meet tetrahedra at both ends alternate with prisms that meet octahedra at both ends.

The gyroelongated triangular prismatic tiling has the same vertex figure as one of the plain prismatic tilings; the two may be derived from the gyrated and plain triangular prismatic tilings, respectively, by inserting layers of cubes.

{|class="wikitable"
!Referenced<br/>indices
!symbol
!Honeycomb name
!cell types (# at each vertex)
!Solids<br/>(Partial)
!Frames<br/>(Perspective)
![[vertex figure]]
|- 
|J<sub>52</sub><br/>A<sub>2'</sub><br/>G<sub>2</sub><br/>O<sub>22</sub>
|h{4,3,4}:g
|align=center|[[gyrated alternated cubic honeycomb|gyrated alternated cubic]] (gytoh)
|align=center|[[tetrahedron]] (8)<br/>[[octahedron]] (6)
|[[File:Gyrated alternated cubic honeycomb.png|70px]]
|[[File:Gyrated alternated cubic.png|100px]]
|[[File:Gyrated alternated cubic honeycomb verf.png|80px]]<br/> [[triangular orthobicupola]]
|- 
|J<sub>61</sub><br/>A<sub>?</sub><br/>G<sub>3</sub><br/>O<sub>24</sub>
|h{4,3,4}:ge
|align=center|[[Gyroelongated alternated cubic honeycomb|gyroelongated alternated cubic]] (gyetoh)
|align=center|[[triangular prism]] (6)<br/>[[tetrahedron]] (4)<br/>[[octahedron]] (3)
|[[File:Gyroelongated alternated cubic honeycomb.png|70px]]
|[[File:Gyroelongated alternated cubic tiling.png|100px]]
|rowspan=2|[[File:Gyroelongated alternated cubic honeycomb verf.png|80px]]
|- 
|J<sub>62</sub><br/>A<sub>?</sub><br/>G<sub>4</sub><br/>O<sub>23</sub>
|h{4,3,4}:e
|align=center|[[Elongated alternated cubic honeycomb|elongated alternated cubic]] (etoh)
|align=center|[[triangular prism]] (6)<br/>[[tetrahedron]] (4)<br/>[[octahedron]] (3)
|[[File:Elongated alternated cubic honeycomb.png|70px]]
|[[File:Elongated alternated cubic tiling.png|80px]]
|- 
|J<sub>63</sub><br/>A<sub>?</sub><br/>G<sub>12</sub><br/>O<sub>12</sub>
|{3,6}:g × {∞}
|align=center|[[Gyrated triangular prismatic honeycomb|gyrated triangular prismatic]] (gytoph)
|align=center|[[triangular prism]] (12)
|[[File:Gyrated triangular prismatic honeycomb.png|70px]]
|[[File:Gyrated triangular prismatic tiling.png|100px]]
|[[File:Gyrated triangular prismatic honeycomb verf.png|80px]]
|- 
|J<sub>64</sub><br/>A<sub>?</sub><br/>G<sub>15</sub><br/>O<sub>13</sub>
|{3,6}:ge × {∞}
|align=center|[[gyroelongated triangular prismatic honeycomb|gyroelongated triangular prismatic]] (gyetaph)
|align=center|[[triangular prism]] (6)<br/>[[cube]] (4)
|[[File:Gyroelongated triangular prismatic honeycomb.png|70px]]
|[[File:Gyroelongated triangular prismatic tiling.png|100px]]
|[[File:Gyroelongated alternated triangular prismatic honeycomb verf.png|80px]]
|}