Gyroelongated Pentagonal Bicupola

Author

Eric W. Weisstein
September 15, 2023

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Polyhedra/GyroelongatedPentagonalBicupola.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/GyroelongatedPentagonalBicupola.html.

©2023 Wolfram Research, Inc. except for portions noted otherwise

Polyhedron

PolyhedronData

PolyhedronData["GyroelongatedPentagonalBicupola","Orientations"]

PolyhedronData["GyroelongatedPentagonalBicupola"]

Netlib

PolyhedronName[JohnsonSolid[46]]

Show[Graphics3D[Polyhedron[JohnsonSolid[46]]],Boxed->False]

Net

PolyhedronData["GyroelongatedPentagonalBicupola","Net"]

PolyhedronData["GyroelongatedPentagonalBicupola","Net","Colored"]

Properties

Initialization

<<MathWorld`Polyhedra`

p=PolyhedronData[pname="GyroelongatedPentagonalBicupola","Polyhedron"]

vol=PolyhedronData[pname,"Volume"]

Centroid

Graphics3D[{AbsolutePointSize[10],
Point[{0,0,0}],{Blue,Point[PolyhedronData[pname,"Centroid"]]},Opacity[.2],PolyhedronData[pname,"GraphicsComplex"]}]

PolyhedronData[pname,"Centroid"]

RegionCentroid[p]//RootReduce//Timing

PolyhedronCentroid[p]//RootReduce//Timing

Circumsphere

PolyhedronData[pname,"Circumsphere"]

Circumsphere[p]

sphere=MyCircumsphere[p]

Convex

ConvexPolyhedronQ[p]

DihedralAngles

PolyhedronData[pname,"DihedralAngles"]//Tally

DihedralAngles[p]//FullSimplify//Tally

EdgeLengths

PolyhedronData[pname,"EdgeLengths"]

PolyhedronData[pname,"Lines"]/.Line[l_]:>EuclideanDistance@@l//FullSimplify//Union//Quiet

Faces

GeneralizedDiameter

PolyhedronData[pname,"GeneralizedDiameter"]

GeneralizedDiameter[p]//FullSimplify//Quiet

InertiaTensor

PolyhedronData[pname,"InertiaTensor"]

((MomentOfInertia[p,{0,0,0}])/(Volume[p]))//RootReduce//Timing

PolyhedronInertiaTensor[p]//Timing

Insphere

PolyhedronData[pname,"Insphere"]

Insphere[p]

sphere=MyInsphere[p]

MeanCylindricalRadius

PolyhedronData[pname,"MeanCylindricalRadius"]

N[%]

((NIntegrate[(Sqrt[(x^2)+(y^2)]),{x,y,z}∈p])/vol)

ClosestMeanCylindricalRadius[%]

Integrate over polyhedron

(rxy=((Integrate[(Sqrt[(x^2)+(y^2)]),{x,y,z}∈p])/vol)//FullSimplify)

N[rxy]

Divergence theorem

(rxy=MeanCylindricalRadius[p,"Simplification"->FullSimplify,Debug->True])//Timing

N[rxy]

LogSimplify[rxy]//FullSimplify

CAD

cad=CylindricalDecomposition[PolyhedronData[pname,"RegionFunction"][x,y,z],{x,y,z},"Function"]

((NIntegrate[(Sqrt[(x^2)+(y^2)])Boole[cad],{x,y,z}∈FullRegion[3]])/vol)

(rxy=((Integrate[(Sqrt[(x^2)+(y^2)])Boole[cad],{x,y,z}∈FullRegion[3]])/vol))//Timing

CAD over  1/10

reg=FullSimplify[PolyhedronData[pname,"RegionFunction"][x,y,z]&&0<y<Tan[Pi/5]x]

cad=CylindricalDecomposition[reg,{x,y,z},"Function"]

10((NIntegrate[(Sqrt[(x^2)+(y^2)])Boole[cad],{x,y,z}∈FullRegion[3]])/vol)

(rxy=10((Integrate[(Sqrt[(x^2)+(y^2)])Boole[cad],{x,y,z}∈FullRegion[3]])/vol))//Timing

N[rxy]

LogSimplify[rxy]//FullSimplify

MeanSquareCylindricalRadius

PolyhedronData[pname,"MeanSquareCylindricalRadius"]

N[%]

((NIntegrate[(x^2)+(y^2),{x,y,z}∈p])/vol)

Integrate over Polyhedron

(rxy2=((Integrate[(x^2)+(y^2),{x,y,z}∈p])/vol)//FullSimplify)

N[rxy2]

MeanSphericalRadius

PolyhedronData[pname,"MeanSphericalRadius"]

((NIntegrate[(Sqrt[(x^2)+(y^2)+(z^2)]),{x,y,z}∈p])/vol)

ClosestMeanSphericalRadius[%]

Integrate over polyhedron

(rxyz=((Integrate[(Sqrt[(x^2)+(y^2)+(z^2)]),{x,y,z}∈p])/vol))//Timing

N[rxyz]

Divergence theorem

(rxyz=MeanSphericalRadius[p,"Simplification"->FullSimplify,Debug->True])//Timing

N[rxyz]

LogSimplify[rxyz]//FullSimplify

CAD

cad=CylindricalDecomposition[PolyhedronData[pname,"RegionFunction"][x,y,z],{x,y,z},"Function"]

((NIntegrate[(Sqrt[(x^2)+(y^2)+(z^2)])Boole[cad],{x,y,z}∈FullRegion[3]])/vol)

(rxyz=((Integrate[(Sqrt[(x^2)+(y^2)+(z^2)])Boole[cad],{x,y,z}∈FullRegion[3]])/vol))//Timing

N[rxyz,20]

rxysimp1=ResourceFunction["LogSimplify"][rxy]//FullSimplify

CAD over  1/10

reg=FullSimplify[PolyhedronData[pname,"RegionFunction"][x,y,z]&&0<y<Tan[Pi/5]x]

cad=CylindricalDecomposition[reg,{x,y,z},"Function"]

10((NIntegrate[(Sqrt[(x^2)+(y^2)+(z^2)])Boole[cad],{x,y,z}∈FullRegion[3]])/vol)

(rxyz=10((Integrate[(Sqrt[(x^2)+(y^2)+(z^2)])Boole[cad],{x,y,z}∈FullRegion[3]])/vol))//Timing

N[rxyz,20]

rxysimp1=LogSimplify[rxy]//FullSimplify

Boole Integrate doing z integral first

{{xmin,xmax},{ymin,ymax},{zmin,zmax}}=CoordinateBounds[p]

ineq=PolyhedronData[pname,"RegionFunction"][x,y,z]

(i1=Integrate[Boole[ineq](Sqrt[(x^2)+(y^2)+(z^2)]),{z,zmin,zmax}])//Timing

NIntegrate[(i1/vol),{x,xmin,xmax},{y,ymin,ymax}]

(i2=Integrate[(i1/vol),{x,xmin,xmax},{y,ymin,ymax}])//Timing

MeanSquareSphericalRadius

PolyhedronData[pname,"MeanSquareSphericalRadius"]

((NIntegrate[(x^2)+(y^2)+(z^2),{x,y,z}∈p])/vol)

Integrate over polyhedron

(rxy2=((Integrate[(x^2)+(y^2)+(z^2),{x,y,z}∈p])/vol)//FullSimplify)

N[rxy2]

Midsphere

sphere=PolyhedronData[pname,"Midsphere"]

(sphere=Midsphere[p,"Simplification"->FullSimplify])//Timing

SurfaceArea

PolyhedronData[pname,"SurfaceArea"]

RootReduce[%]

SurfaceArea[p]//RootReduce//Timing

Total[Area/@PolyhedronData[pname,"Polygons"]]//RootReduce//Timing

VertexSubsetHulls

PolyhedronData[pname,"VertexSubsetHulls"]

Platonic

(h=VertexSubsetHulls[p,"Platonic","Skip"->{}])//Timing

Volume

PolyhedronData[pname,"Volume"]

Volume[p]//FullSimplify

PolyhedronVolume[p,Method->"GaussLaw"]//FullSimplify

Construction

PolyhedronData["PentagonalCupola"]

Min[Last/@PolyhedronData["PentagonalCupola","VertexCoordinates"]]

Min[Last[PolyhedronData[{"Antiprism",10},"VertexCoordinates"]]]//ToRadicals//FullSimplify

dz=Max[Last/@PolyhedronData[{"Antiprism",10},"VertexCoordinates"]]

Graphics3D[g={PolyhedronData[{"Antiprism",10},"Faces"],Rotate[Translate[PolyhedronData["PentagonalCupola","Faces"],{0,0,dz}],π/10,{0,0,1}],
PolyhedronData["PentagonalCupola","Faces"]/.GraphicsComplex[x_,y__]:>GraphicsComplex[{#[[1]],#[[2]],-dz-#[[3]]}&/@x,y]}]

(v=Union[Flatten[Flatten[Normal/@g][[All,1]],1]//Chop,SameTest->(PossibleZeroQ[Norm[#1-#2]]&)])//Length//Quiet

poly2=ConvexHull3D[FullSimplify[v]];

Graphics3D[poly2]

SkeletonGraph/@{poly2,Flatten[Normal[PolyhedronData["GyroelongatedPentagonalBicupola","Faces"]]]}

FastIsomorphicQ@@%

p=ToRadicals[FullSimplify[poly2]]//Simplify

p={Polygon[{{(1/2) (-1-(Sqrt[5])),0,(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/2) (Sqrt[5+2 (Sqrt[5])]),-(1/2),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/8) (((1+(Sqrt[5])))^2),-(1/2) (Sqrt[(1/2) (5+(Sqrt[5]))]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])}}],Polygon[{{(1/2) (-1-(Sqrt[5])),0,(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/2) (Sqrt[5+2 (Sqrt[5])]),(1/2),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/2) (Sqrt[5+2 (Sqrt[5])]),-(1/2),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])}}],Polygon[{{(1/2) (-1-(Sqrt[5])),0,(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/8) (((1+(Sqrt[5])))^2),(Sqrt[(5/8)+((Sqrt[5])/8)]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/2) (Sqrt[5+2 (Sqrt[5])]),(1/2),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])}}],Polygon[{{(1/2) (-1-(Sqrt[5])),0,(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{(1/4) (-1-(Sqrt[5])),(1/2) (Sqrt[(1/10) (5-(Sqrt[5]))]),(Sqrt[(1/10) (5-(Sqrt[5]))])+(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/8) (((1+(Sqrt[5])))^2),(Sqrt[(5/8)+((Sqrt[5])/8)]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])}}],Polygon[{{-(1/2) (Sqrt[5+2 (Sqrt[5])]),-(1/2),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/2) (Sqrt[(1/2) (5+(Sqrt[5]))]),(1/4) (-3-(Sqrt[5])),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/8) (((1+(Sqrt[5])))^2),-(1/2) (Sqrt[(1/2) (5+(Sqrt[5]))]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])}}],Polygon[{{-(1/2) (Sqrt[5+2 (Sqrt[5])]),-(1/2),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/2) (Sqrt[1+(2/(Sqrt[5]))]),-(1/2),-(Sqrt[(1/10) (5-(Sqrt[5]))])-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/2) (Sqrt[(1/2) (5+(Sqrt[5]))]),(1/4) (-3-(Sqrt[5])),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])}}],Polygon[{{-(1/2) (Sqrt[5+2 (Sqrt[5])]),(1/2),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/8) (((1+(Sqrt[5])))^2),(Sqrt[(5/8)+((Sqrt[5])/8)]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/2) (Sqrt[(1/2) (5+(Sqrt[5]))]),(1/4) (3+(Sqrt[5])),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])}}],Polygon[{{-(1/2) (Sqrt[5+2 (Sqrt[5])]),(1/2),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/2) (Sqrt[(1/2) (5+(Sqrt[5]))]),(1/4) (3+(Sqrt[5])),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/2) (Sqrt[1+(2/(Sqrt[5]))]),(1/2),-(Sqrt[(1/10) (5-(Sqrt[5]))])-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])}}],Polygon[{{-(1/8) (((1+(Sqrt[5])))^2),-(1/2) (Sqrt[(1/2) (5+(Sqrt[5]))]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/2) (Sqrt[(1/2) (5+(Sqrt[5]))]),(1/4) (-3-(Sqrt[5])),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/2),-(1/2) (Sqrt[5+2 (Sqrt[5])]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])}}],Polygon[{{-(1/8) (((1+(Sqrt[5])))^2),-(1/2) (Sqrt[(1/2) (5+(Sqrt[5]))]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/2),-(1/2) (Sqrt[5+2 (Sqrt[5])]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/2),-(1/2) (Sqrt[1+(2/(Sqrt[5]))]),(Sqrt[(1/10) (5-(Sqrt[5]))])+(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])}}],Polygon[{{-(1/8) (((1+(Sqrt[5])))^2),(Sqrt[(5/8)+((Sqrt[5])/8)]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/2),(1/2) (Sqrt[5+2 (Sqrt[5])]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/2) (Sqrt[(1/2) (5+(Sqrt[5]))]),(1/4) (3+(Sqrt[5])),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])}}],Polygon[{{-(1/2) (Sqrt[(1/2) (5+(Sqrt[5]))]),(1/4) (-3-(Sqrt[5])),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{0,(1/2) (-1-(Sqrt[5])),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/2),-(1/2) (Sqrt[5+2 (Sqrt[5])]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])}}],Polygon[{{-(1/2) (Sqrt[(1/2) (5+(Sqrt[5]))]),(1/4) (3+(Sqrt[5])),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{-(1/2),(1/2) (Sqrt[5+2 (Sqrt[5])]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{0,(1/2) (1+(Sqrt[5])),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])}}],Polygon[{{-(1/2),-(1/2) (Sqrt[5+2 (Sqrt[5])]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{0,(1/2) (-1-(Sqrt[5])),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{(1/2),-(1/2) (Sqrt[5+2 (Sqrt[5])]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])}}],Polygon[{{-(1/2),(1/2) (Sqrt[5+2 (Sqrt[5])]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{0,(Sqrt[(1/10) (5+(Sqrt[5]))]),(Sqrt[(1/10) (5-(Sqrt[5]))])+(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{(1/2),(1/2) (Sqrt[5+2 (Sqrt[5])]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])}}],Polygon[{{-(1/2),(1/2) (Sqrt[5+2 (Sqrt[5])]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{(1/2),(1/2) (Sqrt[5+2 (Sqrt[5])]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{0,(1/2) (1+(Sqrt[5])),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])}}],Polygon[{{0,(1/2) (-1-(Sqrt[5])),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{(1/2) (Sqrt[(1/10) (5-(Sqrt[5]))]),(1/4) (-1-(Sqrt[5])),-(Sqrt[(1/10) (5-(Sqrt[5]))])-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{(Sqrt[(5/8)+((Sqrt[5])/8)]),(1/4) (-3-(Sqrt[5])),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])}}],Polygon[{{0,(1/2) (-1-(Sqrt[5])),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{(Sqrt[(5/8)+((Sqrt[5])/8)]),(1/4) (-3-(Sqrt[5])),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{(1/2),-(1/2) (Sqrt[5+2 (Sqrt[5])]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])}}],Polygon[{{0,(1/2) (1+(Sqrt[5])),-(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{(1/2),(1/2) (Sqrt[5+2 (Sqrt[5])]),(1/4) (Sqrt[4-(64/((((Sqrt[2])+(Sqrt[10])+2 (Sqrt[5-(Sqrt[5])])))^2))])},{(Sqrt[(5/8)+((Sqrt[5])/8)]),(1/4) (3+(Sqrt[5])),-(1/4) 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Graphics3D[{FaceForm[Blue,Red],Orient[p]}]

PolyhedronData

PolyhedronDataString[Orient[p],
"StandardForm"->"GyroelongatedPentagonalBicupola",
"Name"->"gyroelongated pentagonal bicupola",
"AlternateStandardNames"->{"J46",{"Johnson",46}},
"AlternateNames"->{"J46"},
"NotationRules"->{"Johnson"->46},
"Classes"->{"Convex","Johnson","Equilateral"},
TimeConstraint->30,
Debug->True]