Being a theoretical physicist, I always have a great respect for [Spherical Cow][1]. So I thought about making one myself. I am not sure how can I create (something considered to be the simplest!) this marvel.

One possible way could be using the `ExampleData` for `Cow` and map it on a sphere - something like

 Show[ExampleData[{"Geometry3D", "Cow"}], 
 Graphics3D[Sphere[{-.1, 0, 0.05}, .25]]]

[![enter image description here][2]][2]

I was wondering if there is a way to apply a continuous deformation to the data to get the final sphere (like blowing a balloon).

Another possible way (which is probably the Spherical cow approach of making a Spherical cow) is to map an image of a cow on a sphere.

 face = Import["http://cliparts.co/cliparts/6Ty/ogn/6TyognE8c.png"]

[![enter image description here][3]][3]

 cow = Graphics[{Disk[10 {RandomReal[], RandomReal[]}, RandomReal[]] & /@ Range[20],
 Inset[face]}, AspectRatio -> 1,ImageSize -> 500];

 ParametricPlot3D[{Cos[u] Sin[v], Sin[u] Sin[v], Cos[v]}, {u, 0, 2 Pi},
 {v, 0, Pi}, Mesh -> None, PlotPoints -> 100, 
 TextureCoordinateFunction -> ({#4, 1 - #5} &), Boxed -> False, 
 PlotStyle -> Texture[Show[cow, ImageSize -> 1000]], 
 Lighting -> "Neutral", Axes -> False, RotationAction -> "Clip"]

[![enter image description here][4]][4]

Then it is difficult to manage the legs and the tail.


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**Fixed volume cow**

Based (copying) on [andre's][5] answer here is a modification.

First, we calculate the volume of the cow and the radius of equivalent sphere

 Vcow = Integrate[1, {x, y, z} ∈ ExampleData[{"Geometry3D", "Cow"}, "MeshRegion"]]
 Rcow = (3/(4 Pi) Vcow)^(1/3)

Now insert `Rcow` in the scaing

 Manipulate[cow /. GraphicsComplex[array1_, rest___] :> 
 GraphicsComplex[(# ((Norm[#]/Rcow)^-coeff)) & /@ array1, rest],
 {{coeff, .25}, 0, 1}]

However, if you calculate the volume of the new Spherical Cow with the same method you will not get `Vcow`, because of the fact that on this sphere, several layers are overlapping on each other.

 [1]: https://en.wikipedia.org/wiki/Spherical_cow
 [2]: https://i.sstatic.net/mO7IT.png
 [3]: https://i.sstatic.net/XKHOp.png
 [4]: https://i.sstatic.net/0qhSg.png
 [5]: http://mathematica.stackexchange.com/a/125057/8070