Implicit Solid Model - Thing 1 Free 3D print model

Modeled implicitly (the shape is completely described with an equation) via Mathematica using basic geometries and Boolean Operations.

The main shape is created with a Boolean Addition of a Mobius Strip to a Sphere.

(Boolean Join)
join[f, g] := Min[f, g]
(Boolean Cut)
cut[f, g] := Max[f, -g]

(Translations)
transX [f, s] := f /. x -> (x - s)
transY [f, s] := f /. y -> (y - s)
transZ[f, s] := f /. z -> (z - s)

(Rotate)
rotateRZ[f, a] := f /. {x -> xCos[a] + ySin[a], y -> -xSin[a] + yCos[a]}
rotateZ[f, a] := rotateRZ[f, d2R[a]]

(Declaring a Primitive Geometry: Sphere)
sphere[rad_] := x^2 + y^2 + z^2 - rad^2

(Declaring a Primitive Geometry: Mobius strip - http://www.wolframalpha.com/input/?i=mobius+strip+Cartesian+equation)
mobius[a_] := -a^2 y - 2 a x z + x^2 y - 2 x^2 z + y^3 - 2 y^2 z +
y z^2

(Creating a geometry: muckabout3)
muckabout3 = cut[sphere[2.75], mobius[3]]

(Creating a geometry: trasn2rotatma3)
rotatemuckabout3 = rotateZ[muckabout3, 180]
transrotatema3 = transY[rotatemuckabout3, -0.5]
trans2rotatema3 = transX[transrotatema3, 0.5]

(Creating a geometry: trans2rotatma13)
transrotatema13 = transY[muckabout3, 0.5]
trans2rotatema13 = transX[transrotatema13, -0.5]

(Joining two geometries together)
joinedmuckabout3 = join[trans2rotatema13, trans2rotatema3]

(Creating a geometry: transrttma32)
muckabout32 = cut[sphere[6], mobius[3]]
rotatemuckabout32 = rotateZ[muckabout32, 180]
transrotatema32 = transX[rotatemuckabout32, 3]
transrtransma32 = transY[transrotatema32, 1]
transrttma32 = transZ[transrtransma32, -2.75]

(Joining two geometries together)
joinmuck3s = join[joinedmuckabout3, transrttma32]

(plot the model for a preview)
plt = ContourPlot3D[joinmuck3s == 0, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}

(export your model as an STL file)
Export[ISMmodel1.stl, plt, STL]

Max[-7.5625 + x^2 + y^2 + z^2, 9 y - x^2 y - y^3 + 6 x z + 2 x^2 z + 2 y^2 z - y z^2]
Max[-7.5625 + x^2 + y^2 + z^2, -9 y + x^2 y + y^3 - 6 x z + 2 x^2 z + 2 y^2 z + y z^2]
Max[-7.5625 + x^2 + (0.5 + y)^2 + z^2, -9 (0.5 + y) + x^2 (0.5 + y) + (0.5 + y)^3 - 6 x z + 2 x^2 z + 2 (0.5 + y)^2 z + (0.5 + y) z^2]
Max[-7.5625 + (-0.5 + x)^2 + (0.5 + y)^2 + z^2, -9 (0.5 + y) + (-0.5 + x)^2 (0.5 + y) + (0.5 + y)^3 - 6 (-0.5 + x) z + 2 (-0.5 + x)^2 z + 2 (0.5 + y)^2 z + (0.5 + y) z^2]
Max[-7.5625 + x^2 + (-0.5 + y)^2 + z^2, 9 (-0.5 + y) - x^2 (-0.5 + y) - (-0.5 + y)^3 + 6 x z + 2 x^2 z + 2 (-0.5 + y)^2 z - (-0.5 + y) z^2]
Max[-7.5625 + (0.5 + x)^2 + (-0.5 + y)^2 + z^2, 9 (-0.5 + y) - (0.5 + x)^2 (-0.5 + y) - (-0.5 + y)^3 + 6 (0.5 + x) z + 2 (0.5 + x)^2 z + 2 (-0.5 + y)^2 z - (-0.5 + y) z^2]
Min[Max[-7.5625 + (0.5 + x)^2 + (-0.5 + y)^2 + z^2, 9 (-0.5 + y) - (0.5 + x)^2 (-0.5 + y) - (-0.5 + y)^3 + 6 (0.5 + x) z + 2 (0.5 + x)^2 z + 2 (-0.5 + y)^2 z - (-0.5 + y) z^2], Max[-7.5625 + (-0.5 + x)^2 + (0.5 + y)^2 + z^2, -9 (0.5 + y) + (-0.5 + x)^2 (0.5 + y) + (0.5 + y)^3 - 6 (-0.5 + x) z + 2 (-0.5 + x)^2 z + 2 (0.5 + y)^2 z + (0.5 + y) z^2]]
Max[-36 + x^2 + y^2 + z^2, 9 y - x^2 y - y^3 + 6 x z + 2 x^2 z + 2 y^2 z - y z^2]
Max[-36 + x^2 + y^2 + z^2, -9 y + x^2 y + y^3 - 6 x z + 2 x^2 z + 2 y^2 z + y z^2]
Max[-36 + (-3 + x)^2 + y^2 + z^2, -9 y + (-3 + x)^2 y + y^3 - 6 (-3 + x) z + 2 (-3 + x)^2 z + 2 y^2 z + y z^2]
Max[-36 + (-3 + x)^2 + (-1 + y)^2 + z^2, -9 (-1 + y) + (-3 + x)^2 (-1 + y) + (-1 + y)^3 - 6 (-3 + x) z + 2 (-3 + x)^2 z + 2 (-1 + y)^2 z + (-1 + y) z^2]
Max[-36 + (-3 + x)^2 + (-1 + y)^2 + (2.75 + z)^2, -9 (-1 + y) + (-3 + x)^2 (-1 + y) + (-1 + y)^3 - 6 (-3 + x) (2.75 + z) + 2 (-3 + x)^2 (2.75 + z) + 2 (-1 + y)^2 (2.75 + z) + (-1 + y) (2.75 + z)^2]
Min[Max[-7.5625 + (0.5 + x)^2 + (-0.5 + y)^2 + z^2, 9 (-0.5 + y) - (0.5 + x)^2 (-0.5 + y) - (-0.5 + y)^3 + 6 (0.5 + x) z + 2 (0.5 + x)^2 z + 2 (-0.5 + y)^2 z - (-0.5 + y) z^2], Max[-7.5625 + (-0.5 + x)^2 + (0.5 + y)^2 + z^2, -9 (0.5 + y) + (-0.5 + x)^2 (0.5 + y) + (0.5 + y)^3 - 6 (-0.5 + x) z + 2 (-0.5 + x)^2 z + 2 (0.5 + y)^2 z + (0.5 + y) z^2], Max[-36 + (-3 + x)^2 + (-1 + y)^2 + (2.75 + z)^2, -9 (-1 + y) + (-3 + x)^2 (-1 + y) + (-1 + y)^3 - 6 (-3 + x) (2.75 + z) + 2 (-3 + x)^2 (2.75 + z) + 2 (-1 + y)^2 (2.75 + z) + (-1 + y) (2.75 + z)^2]]