Typically you fold a flexagon by folding together adjacent leaves.
However, sometimes you're required to interleave the template in order to fold it into a particular state.
See http://tech.groups.yahoo.com/group/Flexagon_Lovers/message/314
for some notes on interleaf foldings for point flexagons.
This page describes interleaf folding of edge flexagons.
Key points:
 It's often possible to infterleaf fold an edge flexagon into states you can't flex to otherwise
 You can predict these extra states by looking for nested hinges in the corresponding one sector flexagon, aka point flexagon
 These extra states require interleaf folding across multiple sectors
 It's possible to fold a flexagon such that the template for each sector connects to itself rather than the other sectors
 It's possible to have a face where no adjacent pair of topmost leaves come from the same sector
 A pat no longer consists simply of consecutive leaves from the underlying template
Note that, as with a traditional folding and the pinch flex,
any time leaves are facetoface using an interleaf folding, they will have the same number on them.
The main difference is that, instead of getting there by always folding adjacent sides together
(where folding adjacent a's together may make it so b's are now adjacent),
sometimes you must interleave different parts of the template in order to achieve facetoface numberings.
Hexahexaflexagon
The first example is a 6 sided flexagon.
Below is the state diagram for the point flexagon.
It shows which sides are accessible from which sides.
For example, the line from side 1 to side 2 means that you can flex from side 1 to side 2 and back again.
The red dashed line indicates that the hinges from one side are nested inside the hinges for another side.
To make the point flexagon:
 Click on the template to get the large version
 Cut it out and prefold along the dotted lines
 Copy the small numbers onto the back
 Fold 6 on 6, 5 on 5, 4 on 4 and 3 on 3
 Tape together the hinges from the first and last leaf
To make the corresponding edge flexagon:
 Click on the template to get the large version
 Cut out the two templates and prefold along the dashed lines
 Copy the small numbers onto the back
 For the traditional folding, tape leaf 3/5 to leaf 1/5 along the dotted edges
 Next fold the adjacent 6's together, followed by adjacent 5's, 4's and 3's
 Tape together the dashed edges of the first and last leaves
From this position, you'll find that anywhere there's a solid black line between two numbers in the above diagram,
you can pinch flex to a state with one of those numbers on one side and the other on the opposite side.
For example, the line from 1 to 3 means you flex to a state with 1 on one side and 3 on the other.
However, you can't pinch flex to any of the states with a red line.
For example, you can't flex to a state with 4 on one side and 5 on the other.
To get to this state, untape the edges to get it back to two separate templates, then:
 Lay one strip on top of the other such that the 1’s, 2’s and 3’s are back to back with like numbers.
 Next fold each of the adjacent pairs of 6’s against each other (as you would fold a trihexaflexagon).
 You’ll now have two pairs of triangles side by side that need to be taped together.
 From here you can flex between 4/5, 5/6 and 6/4, but no other states are accessible.
8 sided hexaflexagon
The next example has 8 sides and lots of nested hinges.
One of the interesting things about this pattern is that is has a doubly nested hinge between sides 7 and 8.
When you fold the edge flexagon such that sides 7 and 8 are opposite each other,
you'll find that you've connected each sector back to itself.
You have three independent loops interleaved together.
To make the point flexagon:
 Click on the template to get the large version
 Cut it out and prefold along the dotted lines
 Copy the small numbers onto the back
 Fold 8 on 8, 7 on 7, 6 on 6, 5 on 5, 4 on 4 and 3 on 3
 Tape together the hinges from the first and last leaf
To make the corresponding edge flexagon:
 Click on the template to get the large version
 Cut out the three templates and prefold along the dashed lines
 Copy the small numbers onto the back
 For the traditional folding, tape leaf 8/3 on the first strip to leaf 1/2 on the second strip along the dotted edges
 Tape leaf 8/3 on the second strip to leaf 1/2 on the third strip along the dotted edges
 Next fold the adjacent 8's together, followed by adjacent 7's, 6's, 5's, 4's and 3's
 Tape together the dashed edges of the first and last leaves
 From here, all the states represented by black lines are accessible
To get to any of the states represented by the red dashed lines, take the flexagon back apart into three strips of paper.
Though it's tricky, you can fold into state 1/5, 3/6, 3/7, 4/8, 6/7 or 7/8.
States 1/5, 4/8 and 7/8 are singular; you can't pinch flex at all from these positions.
But you can flex between 3/6, 3/7 and 6/7.
Directions for folding to state 3/7 (difficult):
 For each of the three strips, fold 8 on 8 and 7 on 7
 Fold the adjacent 4 and 5 together
 Each strip should now have one pat with 4 on one side and 5 on the other and a pat with 4 and 5 on the inside
 Take two strips and wrap these 4/5 pairs together such that the outside 4 from one strip is against the inside 4 from the other and the outside and inside 5's are facetoface
 You should now have four 6's in a row on one side and, after tucking one end pat under the other so the 1's are facetoface, four 3's on the other side
 Take the final strip and wrap its inside 4/5 around the outside 4/5 in a similar fashion
 Tuck the leaf on the final strip labeled 1/2 under the 3 such that the 1's are facetoface and the 2's are facetoface
 Thread the other end of the final strip under the 6's, putting the 4's and 5's facetoface
 Tuck the 1 that's on top under the leaf labeled 3, making it so one side of the hexagon has six 3's and the other side has six 6's
 To complete it, tape the outside edge of the 3's that are only connected along one edge to the leaf labeled 1/2 below it
Folding to the other states is equally tricky.
The basic approach is that you start by folding each of the three strips into a piece of the hexagon.
You may need to temporarily fold nonlike numbers together, but you'll eventually slide another piece in there so that all facetoface numbers match.
It's interesting to note that the state diagram of the edge flexagon using the pinch flex is fully predicted by the state diagram of the corresponding point flexagon.
All transitions not involving nested hinges can be pinch flexed to if you fold to one of those states.
Any transitions involving nested hinges require taking apart the flexagon and reassembling it using an interleaf folding.
8 sided square tetraflexagon
The following flexagons have 8 sides.
To make the point flexagon:
 Click on the template to get the large version
 Cut it out and prefold along the dotted lines
 Copy the small numbers onto the back
 Fold 8 on 8, 7 on 7, 6 on 6, 5 on 5, 4 on 4 and 3 on 3
 Tape together the hinges from the first and last leaf
From the state diagram of the point flexagon, you can see that the edge flexagon allows you to pinch flex between states 1/2, 1/3, 1/7, 1/8, 2/4, 2/5, 3/4, 3/6, 5/8 and 6/7
and the only way to get to states 4/5 or 4/6 is to fold directly to them.
To make the corresponding edge flexagon:
 Click on the template to get the large version
 Cut out the two templates and prefold along the dashed lines
 Copy the small numbers onto the back
 For the traditional folding, tape leaf 6/3 on the first strip to leaf 5/2 on the second strip along the dotted edges
 Next fold the adjacent 8's together, followed by adjacent 7's, 6's, 5's, 4's and 3's
 Tape together the dashed edges of the first and last leaves
 From here, all the states represented by black lines are accessible
To fold to state 4/5, disconnect the strips, then:
 Put tape on the dashed edge of the two leaves labeled 6/3
 On each template, fold 8 on 8, 7 on 7 and 6 on 6
 Fold together the adjacent 1 and 3 on each template
 Wrap the internal 1/3 from one template around the external 1/3 from the other so that the 1's are facetoface and the 3's are facetoface, making a square of four smaller squares
 Tuck the pat with 3 on the top under the leaf with 4 on the top so that the 1's are facetoface and the 3's are facetoface
 You should now have four 4's on one side and four 5's on the other
 The tape sticking off sides 6/3 should be attached to the two leaves labeled 5/2
 From here you can pinch flex to state 4/6
Main flexagon page
