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It has a second construction as a uniform honeycomb, [[Schläfli symbol]] {6,(∞,3,∞)}, Coxeter diagram, {{CDD|node_1|6|node|split1-ii|branch}}, with alternating types or colors of cells. In Coxeter notation the half symmetry is [6,∞,6,1<sup>+</sup>] = [6,((∞,3,∞))].
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=== Order-infinite-7 heptagonal honeycomb===
{| class="wikitable" align="right" style="margin-left:10px" width=280
!bgcolor=#efdcc3 colspan=2|Order-infinite-7 heptagonal honeycomb
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|bgcolor=#efdcc3|Type||[[List of regular polytopes#Tessellations of hyperbolic 3-space|Regular honeycomb]]
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|bgcolor=#efdcc3|[[Schläfli symbol]]s||{7,∞,7}
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|bgcolor=#efdcc3|[[Coxeter diagram#Lorentzian groups|Coxeter diagrams]]||{{CDD|node_1|7|node|infin|node|6|node}}
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|bgcolor=#efdcc3|Cells||[[order-5 heptagonal tiling|{7,∞}]] [[File:H2 tiling 27i-4.png|60px]]
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|bgcolor=#efdcc3|Faces||[[heptagon|{7}]]
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|bgcolor=#efdcc3|Edge figure||[[heptagon|{7}]]
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|bgcolor=#efdcc3|Vertex figure||[[Order-7 heptagonal tiling|{∞,7}]] [[File:H2 tiling 27i-4.png|40px]]
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|bgcolor=#efdcc3|Dual||self-dual
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|bgcolor=#efdcc3|[[Coxeter-Dynkin diagram#Lorentzian groups|Coxeter group]]||[7,∞,7]
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|bgcolor=#efdcc3|Properties||Regular
|}
In the [[geometry]] of [[Hyperbolic space|hyperbolic 3-space]], the '''order-infinite-7 heptagonal honeycomb''' (or '''7,∞,7 honeycomb''') is a regular space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]) with [[Schläfli symbol]] {7,∞,7}. It has seven [[infinite-order heptagonal tiling]]s, {7,∞}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many heptagonal tilings existing around each vertex in an [[order-7 heptagonal tiling]] [[vertex arrangement]].
{| class=wikitable
<!--|[[File:Hyperbolic honeycomb 7-i-7 poincare.png|240px]]<BR>[[Poincaré disk model]]-->
|[[File:H3_7i7_UHS_plane_at_infinity.png|240px]]<BR>Ideal surface
|}
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