Acronym squit
Name (line) square tegum,
Waterman polyhedron number 2 wrt. body-centered cubic lattice C3* centered at a hole
Coordinates
  • (1; 0, 0)/2   all changes of sign
  • (0; 1, 1)/2   all changes of sign
Volume 1/3 = 0.333333
Face vector 6, 12, 8
Confer
uniform variant:
oct
general polytopal classes:
Hanner polytopes  

The unit here was chosen as the cube edge of C3*.

By the very definition of Waterman polyhedra, not necessarily all vertices are on the same sphere. In here the 4 equatorial vertices have a circumradius of 1/sqrt(2) = 0.707107, while the 2 polar vertices correspond to a radius of 1/2 = 0.5.


Incidence matrix according to Dynkin symbol

xo ox4oo&#zc   → height = 0, 
                 where c = sqrt(3)/2 = 0.866025
(tegum product of line and square)

o. o.4o.    | 2 * | 4 0 | 4
.o .o4.o    | * 4 | 2 2 | 4
------------+-----+-----+--
oo oo4oo&#c | 1 1 | 8 * | 2  c
.. .x ..    | 0 2 | * 4 | 2  x
------------+-----+-----+--
.. ox ..&#c | 1 2 | 2 1 | 8

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