Content deleted Content added
No edit summary |
|||
Line 301:
|[[File:Hyperbolic honeycomb 6-i-3 poincare.png|240px]]<BR>[[Poincaré disk model]]
|[[File:H3_6i3_UHS_plane_at_infinity.png|240px]]<BR>Ideal surface
|}
{{-}}
=== Order-infinite-3 heptagonal honeycomb===
{| class="wikitable" align="right" style="margin-left:10px"
!bgcolor=#efdcc3 colspan=2|Order-infinite-3 heptagonal honeycomb
|-
|bgcolor=#efdcc3|Type||[[List of regular polytopes#Tessellations of hyperbolic 3-space|Regular honeycomb]]
|-
|bgcolor=#efdcc3|[[Schläfli symbol]]||{7,∞,3}
|-
|bgcolor=#efdcc3|[[Coxeter diagram]]||{{CDD|node_1|7|node|infin|node|3|node}}
|-
|bgcolor=#efdcc3|Cells||[[infinite-order heptagonal tiling|{7,∞}]] [[File:H2_tiling_27i-4.png|80px]]
|-
|bgcolor=#efdcc3|Faces||[[Heptagon|{7}]]
|-
|bgcolor=#efdcc3|[[Vertex figure]]||[[order-3 apeirogonal tiling|{∞,3}]]
|-
|bgcolor=#efdcc3|Dual||[[Order-infinite-7 triangular honeycomb|{3,∞,7}]]
|-
|bgcolor=#efdcc3|[[Coxeter–Dynkin diagram#Ranks 4.E2.80.9310|Coxeter group]]||[7,∞,3]
|-
|bgcolor=#efdcc3|Properties||Regular
|}
In the [[geometry]] of [[Hyperbolic space|hyperbolic 3-space]], the '''order-infinite-3 heptagonal honeycomb''' (or '''7,∞,3 honeycomb''') a regular space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]). Each infinite cell consists of a [[order-7 hexagonal tiling]] whose vertices lie on a [[Hypercycle (geometry)|2-hypercycle]], each of which has a limiting circle on the ideal sphere.
The [[Schläfli symbol]] of the ''order-infinite-3 heptagonal honeycomb'' is {7,∞,3}, with three infinite-order heptagonal tilings meeting at each edge. The [[vertex figure]] of this honeycomb is a order-3 apeirogonal tiling, {∞,3}.
{| class=wikitable
<!--|[[File:Hyperbolic honeycomb 7-i-3 poincare.png|240px]]<BR>[[Poincaré disk model]]-->
|[[File:H3_7i3_UHS_plane_at_infinity.png|240px]]<BR>Ideal surface
|}
| |||