flammParaboloid=DiscretizeGraphics[RevolutionPlot3D[2*Sqrt[(r-1)],{r,1,2}]]
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pts=RandomPoint[flammParaboloid,1000];
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ListPointPlot3D[%]
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ResourceFunction["NonConvexHullMesh"][pts,1]
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MeshConnectivityGraph[%]
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Graph3D[%,GraphLayout"SpringElectricalEmbedding",VertexCoordinatesAutomatic]
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sch=
;
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DelaunayMesh[RandomPoint[flammParaboloid,1000]]
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MeshConnectivityGraph[%]
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RegionBoundary[DelaunayMesh[RandomPoint[flammParaboloid,1000]]]
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MeshConnectivityGraph[%]
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​
NearestNeighborGraph[%173,4]
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NearestNeighborGraph[%173,10]
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SimpleGraph[%]
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TransitiveReductionGraph[%]
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HypergraphDimensionEstimateListList@@@EdgeList

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{3.653±0.006,2.499±0.015,2.409±0.024,2.271±0.035,2.11±0.05,2.00±0.05,1.90±0.06,1.80±0.06,1.68±0.06,1.54±0.06,1.44±0.06,1.38±0.07,1.30±0.07,1.22±0.07,1.14±0.07,1.01±0.06,0.88±0.05}
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ListLinePlot[%]
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DiscretizeGraphics[Disk[]]
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SimpleGraph[NearestNeighborGraph[RandomPoint[%,1000],8]]
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HypergraphDimensionEstimateList[List@@@EdgeList[%]]
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{3.368±0.006,2.382±0.016,2.340±0.026,2.31±0.04,2.20±0.05,2.09±0.06,2.01±0.08,1.92±0.09,1.82±0.10,1.75±0.11,1.65±0.12,1.53±0.13,1.43±0.13,1.32±0.13}
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ListLinePlot[%]
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VoronoiMesh[