Stereographic Projections

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Stereographic Projections

• Geol 3055
• Klein (2000), p. 240-244 246-276

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How a spherical projection is produced
CRYSTAL PROJECTIONS represents the 3-D crystal
shape on 2-D surface

• Imagine a crystal inside a big transparent beach
  ball with a small, bright point of source light.
• Use pinholes to see the light passing through
  perpendicular to all the crystals faces
• Using the light points on each face, mark the
  faces in the inside of the ball (see Fig 6.3 p.
  242 Klein)
• Each face represented by a point is called a face
  pole
• A stereographic projection is half (the northern
  hemisphere) of the spherical projection

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001
Developing a Spherical Projection
-100
0-10
010
100
00-1
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Stereographic projections
Fig 6.3 Spherical projection of an isometric
crystal
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Stereographic projections
Plane of half the spherical projection (N
hemisphere)
Plane of projection -equatorial plane of sphere
Primitive Circle outlining projection -equator
Fig 6.5 Relationship between spherical
stereographic projection
NOTE Line of sight between face poles S pole
produces new POLES
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Stereographic projections
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Stereographic projections
This is a stereographic projection of an
isometric crystal with the faces identified by
Miller indices
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Stereographic projections

• Making stereographic projections of crystals is
  great fun
• unfortunately we will not do this in this class
• But you must know how to read them

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Stereographic projections

• Symmetry elements present
• Two fold axis
• Mirror
• Monoclinic crystal system, 2/m
• Monoclinic prism

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Stereographic projections

• Symmetry elements present
• 3 two-fold axes
• 3 mirrors
• Orthorhombic (2/m2/m2/m)

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Stereographic projections

• Symmetry elements present
• 5 mirrors
• 1 four-fold axis
• 4 two-fold axes
• Tetragonal Crystal system 4/m2/m2/
• Crystal Form is a Ditetragonal bipyramid

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Stereographic projections

• Symmetry elements present
• 7 mirrors
• 6 two-fold axes
• 1 six-fold axis
• Hexagonal crystal system 6/m2/m2/m
• Crystal form is a Dihexagonal bipyramid

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1
1
2
2
3
3
4

• Symmetry elements present
• 3 four-fold axes
• 4 three fold (rotoinversion) axes
• 6 two-fold axes
• 9 mirrors
• Isometric crystal system crystal form is a
  Hexoctahedron

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• Symmetry elements present
• 3 four-fold (rotoinversion) axes
• 4 three fold axes
• 6 mirrors
• Isometric system
• Hexa tetrahedral class