GraphData["DistanceTransitive"]

In[]:=

Out[]=

GraphData["HeawoodGraph"]

In[]:=

Out[]=

Intersection[GraphData["Cage"],GraphData["Cubic"]]

In[]:=

Out[]=

GraphData/@%

In[]:=

Out[]=

GraphNeighborhoodVolumes[1]

In[]:=

{1,4,10,22,46,66,70}

Out[]=

Differences[%]

In[]:=

{3,6,12,24,20,4}

Out[]=

Differences[%]

In[]:=

{3,6,12,-4,-16}

Out[]=

GraphNeighborhoodVolumes[1]

In[]:=

#### https://en.wikipedia.org/wiki/Modular_lattice

https://en.wikipedia.org/wiki/Modular_lattice

https://en.wikipedia.org/wiki/Continuous_geometry

https://www.ams.org/journals/tran/1979-251-00/S0002-9947-1979-0531987-8/S0002-9947-1979-0531987-8.pdf

## Lattice Theory

Lattice Theory

## Projective Space

Projective Space

Definition of discrete version:

any two lines intersect at a point; any two points are connected by a line

any two lines intersect at a point; any two points are connected by a line

#### Multiway systems ↔

Multiway systems ↔

## Foliations

Foliations

If the rule caused states to only go to their neighbors in the multiway layout, then we would have the same conditions as for spacetime .... because there is locality in string space....

Ordering by sortedness.....

All refoliations away from the geodesic foliation will prune the branchial graphs.....