Waterman Polyhedron

the basic series are defined as -
The convex hull of the intersection of a closed ball with the lattice of sphere- center points of a cubic close packing
A Generalized Waterman polyhedron, would include any related ccp structuring, wherein pertinent all space fillers become employed to establish a common/combined lattice point set. This Generalized approach is currently on the agenda, and as of yet, not finished the applicable programming via computer software.
These basic Waterman Polys were made in Early November 2005. The three rows represent Waterman polyhedron from root 1 through root 10 for two of the series below, the 1wn and the 6wn. Also shown, is a third series, based upon consecutive radial sweeps from a cube.

left row is "cubic" - with center of cube series from Generalized approach
            center row is "1wn" - from center of one sphere - the BASIC series of WP
                        right row is "6wn" - with center of octahedral void series from Generalized approach

Photos taken by Bob Malvasio.

The gray polyhedron are all-space-fillers. Faces have been colored as; red - along the 6 x,y,z axis, blue as per the 8 vertex of a cube and yellow as per the 12 mid-points of the edges of a cube. "Gaps" between those three have been appropriately colored as orange, purple and green.
Click on the phrase above the icons below to go to these other sites.

applet by Mark Newbold
[1 to 3000]
all 7 series

Great Stella by Rob Webb [1 to unlimited]
2 of the 7 series

generator by Paul Bourke
[1 to 1000]
4 of the 7 series

write up
by Paul Bourke
ccp matrix schemes depictions
by Maurice Starck
( slow loading...great graphics )

write up
by Maurice Starck

MuPad on-line article
[ inter-reactive ]
by Mirek Majewski
MathWorld write up
by Eric W. Weisstein

by Adrian Rossiter

Adrian Rossiter's site

write-up by Rene K. Muller
1w1 - 1w100

write-up by Rene K. Muller
1w101 - 1w250

removed temporarily due to space concerns

Wikipedia article

missing numbers

edge lengths
maximum and minimum

next release 
4d Waterman
in Great Stella

SpringDance by Alan Ferguson
[ 1-50 eig ]

early work
by Kirby Urner

LynnClaire Dennis poly

Steinmetz-Waterman solids

dice combinations
by Dan Thomasson

ShapeScape by Matt Storz
hex prisms
and w10
inter-locking grids

the first few polyhedron from the basic sphere center series


no spheres at root 14 14


no spheres at root 30 30


no spheres at root 46 46


no spheres at root 56
[rt 14 x 4]
no spheres at root 62 62


no spheres at root 78 78


no spheres at root 94 94


no spheres at root 110 110


Integer sequences related to Waterman polyhedra by Neil J. Sloane.

w1,n series    ORIGIN is center of sphere
A119869 size        A119870 vertex    A119871 faces
A119872 edges     A119873 volumes   
A055039 missing numbers

w6,n series    ORIGIN is at center of 6 sphere cluster...the octahedral void
A119874 size        A119875 vertex    A119876 faces
A119877 edges     A119878 volumes    

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