Snub Disphenoid

Author

Eric W. Weisstein
May 11, 2021

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

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

©2021 Wolfram Research, Inc. except for portions noted otherwise

Solid

PolyhedronData["SnubDisphenoid","Orientations"]

PolyhedronData["SnubDisphenoid"]

Net

PolyhedronData["SnubDisphenoid","Net"]

PolyhedronData["SnubDisphenoid","Net","Colored"]

NetPrintout[PolyhedronData["SnubDisphenoid","Polyhedron"],"SnubDisphenoid.pdf"]

Properties

<<MathWorld`PolyhedronOperations`

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

Centroid

PolyhedronData[pname,"Centroid"]

RegionCentroid[p]//RootReduce

PolyhedronCentroid[p]

Circumsphere

PolyhedronData[pname,"Circumsphere"]

Circumsphere[p]

MyCircumsphere[p]

DihedralAngles

PolyhedronData[pname,"DihedralAngles"]//Tally

RootReduce[%]

DihedralAngles[p]//RootReduce//Tally

Dual

PolyhedronData[pname,"Dual"]

PolyhedronData[pname,"Dual","Name"]

Graphics3D[{Opacity[.5],poly=PolyhedronData[pname,"Polyhedron"],DualPolyhedron[poly]}]

EdgeLengths

PolyhedronData[pname,"EdgeLengths"]

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

Faces

GeneralizedDiameter

PolyhedronData[pname,"GeneralizedDiameter"]

GeneralizedDiameter[p]//RootReduce

Insphere

PolyhedronData[pname,"Insphere"]

Insphere[p]

MyInsphere[p,"Simplification"->FullSimplify,Debug->True]

InertiaTensor

PolyhedronData[pname,"InertiaTensor"]

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

PolyhedronInertiaTensor[p]//RootReduce//Timing

MeanCylindricalRadius

((NIntegrate[(Sqrt[(x^2)+(y^2)]),{x,y,z}∈p])/(PolyhedronData[pname,"Volume"]))

(i=((Integrate[(Sqrt[(x^2)+(y^2)]),{x,y,z}∈p])/(PolyhedronData[pname,"Volume"])))//Timing

N[i]

MeanCylindricalSquareRadius

((NIntegrate[(x^2)+(y^2),{x,y,z}∈p])/(PolyhedronData[pname,"Volume"]))

(i=((Integrate[(x^2)+(y^2),{x,y,z}∈p])/(PolyhedronData[pname,"Volume"]))//RootReduce)//Timing

N[i]

MeanSphericalRadius

((NIntegrate[(Sqrt[(x^2)+(y^2)+(z^2)]),{x,y,z}∈p])/(PolyhedronData[pname,"Volume"]))

(i=((Integrate[(Sqrt[(x^2)+(y^2)+(z^2)]),{x,y,z}∈p])/(PolyhedronData[pname,"Volume"])))//Timing

N[i]

MeanSphericalSquareRadius

((NIntegrate[(x^2)+(y^2)+(z^2),{x,y,z}∈p])/(PolyhedronData[pname,"Volume"]))

(i=((Integrate[(x^2)+(y^2)+(z^2),{x,y,z}∈p])/(PolyhedronData[pname,"Volume"]))//RootReduce)//Timing

N[i]

Midsphere

PolyhedronData[pname,"Midsphere"]

Midsphere[N@p,Method->"PointLineDistance"]//Timing

Midsphere[N@p,Method->"PointsTangentAndPerpendicular"]//Timing

Midsphere[p,Method->"PointLineDistance","Simplification"->RootReduce,Debug->True]//Timing

Midsphere[p,Method->"PointsTangentAndPerpendicular","Simplification"->RootReduce,Debug->True]//Timing

SurfaceArea

PolyhedronData[pname,"SurfaceArea"]

RootReduce[%]

SurfaceArea[p]//RootReduce//Timing

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

VertexSubsetHulls

Platonic

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

Volume

PolyhedronData[pname,"Volume"]

Volume[p]//FullSimplify

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

Perspective projections

Manipulate[PolyhedronProjectionGraph[PolyhedronData["Cuboctahedron","Polyhedron"],{a,b,c}],{a,-1,1},{b,-1,1},{c,-1,1}]

XXX

PolyhedronProjectionGraph[PolyhedronData["DuererSolid","Polyhedron"],]

Construction

PolyhedronData["SnubDisphenoid","VertexCoordinates"]