Acronym editetaf
Name edge-diminished tetaf,
(top base) edge-diminishing of tet-first rotunda of hin
Circumradius sqrt(5/8) = 0.790569
Lace city
in approx. ASCII-art 
    e    	-- s2s o o (line)
         	
T       T	-- s2s2s x (tepe)

  \       \
   \       +-- (squasc)
    +--------- (tet)

where:
e = s2s o (line)
T = s2s2s (tet)

    x2o           
                  
                  
                  
o2x  xo2ox&#x  x2o		-- o3o3x x (inv tepe)

x o o          
               
               
               
               
o x x     x o x		-- o3o3x x (tepe)

  |            \
  |              +-- (trip)
  +----------------- (squasc)
Coordinates
  • (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 0, 1/2)      & all even changes of sign in first 2 coordinates
    (top base, edge of tet)
  • (1/sqrt(8), 1/sqrt(8), -1/sqrt(8), 1/2, 0)     & all even changes of sign in first 3 coordinates resp. change of sign in 4th
    (bottom base, tepe)
coordinates are centered to the bottom base, but obviously also centered at the circumcenter
Face vector 10, 29, 38, 25, 8
Confer
uniform relative:
hin  
related segmentotera:
tetaf  
general polytopal classes:
segmentotera   lace simplices  

Incidence matrix according to Dynkin symbol

xxo oox oxx&#x   → height(2,3) = 1/sqrt(2) = 0.707107
                   height(1,2) = sqrt(3)/2 = 0.866025
                   height(1,3) = 1/2

o.. o.. o..    | 2 * * | 1 2 4 0 0 0 0 0 | 2 1 4 2 2 4 0 0 0 0 0 | 1 2 2 1 4 2 2 0 0 0 | 1 2 2 1 0
.o. .o. .o.    | * 4 * | 0 1 0 1 1 2 0 0 | 1 1 0 0 0 2 1 2 1 2 0 | 1 0 0 0 2 1 2 1 2 1 | 0 1 2 1 1
..o ..o ..o    | * * 4 | 0 0 2 0 0 2 1 1 | 0 0 1 2 2 2 0 1 2 2 1 | 0 1 1 2 1 2 2 1 1 2 | 1 1 1 2 1
---------------+-------+-----------------+-----------------------+---------------------+----------
x.. ... ...    | 2 0 0 | 1 * * * * * * * | 2 0 4 0 0 0 0 0 0 0 0 | 1 2 2 0 4 0 0 0 0 0 | 1 2 2 0 0
oo. oo. oo.&#x | 1 1 0 | * 4 * * * * * * | 1 1 0 0 0 2 0 0 0 0 0 | 1 0 0 0 2 1 2 0 0 0 | 0 1 2 1 0
o.o o.o o.o&#x | 1 0 1 | * * 8 * * * * * | 0 0 1 1 1 1 0 0 0 0 0 | 0 1 1 1 1 1 1 0 0 0 | 1 1 1 1 0
.x. ... ...    | 0 2 0 | * * * 2 * * * * | 1 0 0 0 0 0 1 2 0 0 0 | 1 0 0 0 2 0 0 1 2 0 | 0 1 2 0 1
... ... .x.    | 0 2 0 | * * * * 2 * * * | 0 1 0 0 0 0 1 0 0 2 0 | 1 0 0 0 0 0 2 0 2 1 | 0 0 2 1 1
.oo .oo .oo&#x | 0 1 1 | * * * * * 8 * * | 0 0 0 0 0 1 0 1 1 1 0 | 0 0 0 0 1 1 1 1 1 1 | 0 1 1 1 1
... ..x ...    | 0 0 2 | * * * * * * 2 * | 0 0 0 2 0 0 0 0 2 0 1 | 0 1 0 2 0 2 0 1 0 2 | 1 1 0 2 1
... ... ..x    | 0 0 2 | * * * * * * * 2 | 0 0 0 0 2 0 0 0 0 2 1 | 0 0 1 2 0 0 2 0 1 2 | 1 0 1 2 1
---------------+-------+-----------------+-----------------------+---------------------+----------
xx. ... ...&#x | 2 2 0 | 1 2 0 1 0 0 0 0 | 2 * * * * * * * * * * | 1 0 0 0 2 0 0 0 0 0 | 0 1 2 0 0
... ... ox.&#x | 1 2 0 | 0 2 0 0 1 0 0 0 | * 2 * * * * * * * * * | 1 0 0 0 0 0 2 0 0 0 | 0 0 2 1 0
x.o ... ...&#x | 2 0 1 | 1 0 2 0 0 0 0 0 | * * 4 * * * * * * * * | 0 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
... o.x ...&#x | 1 0 2 | 0 0 2 0 0 0 1 0 | * * * 4 * * * * * * * | 0 1 0 1 0 1 0 0 0 0 | 1 1 0 1 0
... ... o.x&#x | 1 0 2 | 0 0 2 0 0 0 0 1 | * * * * 4 * * * * * * | 0 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
ooo ooo ooo&#x | 1 1 1 | 0 1 1 0 0 1 0 0 | * * * * * 8 * * * * * | 0 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
.x. ... .x.    | 0 4 0 | 0 0 0 2 2 0 0 0 | * * * * * * 1 * * * * | 1 0 0 0 0 0 0 0 2 0 | 0 0 2 0 1
.xo ... ...&#x | 0 2 1 | 0 0 0 1 0 2 0 0 | * * * * * * * 4 * * * | 0 0 0 0 1 0 0 1 1 0 | 0 1 1 0 1
... .ox ...&#x | 0 1 2 | 0 0 0 0 0 2 1 0 | * * * * * * * * 4 * * | 0 0 0 0 0 1 0 1 0 1 | 0 1 0 1 1
... ... .xx&#x | 0 2 2 | 0 0 0 0 1 2 0 1 | * * * * * * * * * 4 * | 0 0 0 0 0 0 1 0 1 1 | 0 0 1 1 1
... ..x ..x    | 0 0 4 | 0 0 0 0 0 0 2 2 | * * * * * * * * * * 1 | 0 0 0 2 0 0 0 0 0 2 | 1 0 0 2 1
---------------+-------+-----------------+-----------------------+---------------------+----------
xx. ... ox.&#x ♦ 2 4 0 | 1 4 0 2 2 0 0 0 | 2 2 0 0 0 0 1 0 0 0 0 | 1 * * * * * * * * * | 0 0 2 0 0
x.o o.x ...&#x ♦ 2 0 2 | 1 0 4 0 0 0 1 0 | 0 0 2 2 0 0 0 0 0 0 0 | * 2 * * * * * * * * | 1 1 0 0 0
x.o ... o.x&#x ♦ 2 0 2 | 1 0 4 0 0 0 0 1 | 0 0 2 0 2 0 0 0 0 0 0 | * * 2 * * * * * * * | 1 0 1 0 0
... o.x o.x&#x ♦ 1 0 4 | 0 0 4 0 0 0 2 2 | 0 0 0 2 2 0 0 0 0 0 1 | * * * 2 * * * * * * | 1 0 0 1 0
xxo ... ...&#x ♦ 2 2 1 | 1 2 2 1 0 2 0 0 | 1 0 1 0 0 2 0 1 0 0 0 | * * * * 4 * * * * * | 0 1 1 0 0
... oox ...&#x ♦ 1 1 2 | 0 1 2 0 0 2 1 0 | 0 0 0 1 0 2 0 0 1 0 0 | * * * * * 4 * * * * | 0 1 0 1 0
... ... oxx&#x ♦ 1 2 2 | 0 2 2 0 1 2 0 1 | 0 1 0 0 1 2 0 0 0 1 0 | * * * * * * 4 * * * | 0 0 1 1 0
.xo .ox ...&#x ♦ 0 2 2 | 0 0 0 1 0 4 1 0 | 0 0 0 0 0 0 0 2 2 0 0 | * * * * * * * 2 * * | 0 1 0 0 1
.xo ... .xx&#x ♦ 0 4 2 | 0 0 0 2 2 4 0 1 | 0 0 0 0 0 0 1 2 0 2 0 | * * * * * * * * 2 * | 0 0 1 0 1
... .ox .xx&#x ♦ 0 2 4 | 0 0 0 0 1 4 2 2 | 0 0 0 0 0 0 0 0 2 2 1 | * * * * * * * * * 2 | 0 0 0 1 1
---------------+-------+-----------------+-----------------------+---------------------+----------
x.o o.x o.x&#x ♦ 2 0 4 | 1 0 8 0 0 0 2 2 | 0 0 4 4 4 0 0 0 0 0 1 | 0 2 2 2 0 0 0 0 0 0 | 1 * * * *
xxo oox ...&#x ♦ 2 2 2 | 1 2 4 1 0 4 1 0 | 1 0 2 2 0 4 0 2 2 0 0 | 0 1 0 0 2 2 0 1 0 0 | * 2 * * *
xxo ... oxx&#x ♦ 2 4 2 | 1 4 4 2 2 4 0 1 | 2 2 2 0 2 4 1 2 0 2 0 | 1 0 1 0 2 0 2 0 1 0 | * * 2 * *
... oox oxx&#x ♦ 1 2 4 | 0 2 4 0 1 4 2 2 | 0 1 0 2 2 4 0 0 2 2 1 | 0 0 0 1 0 2 2 0 0 1 | * * * 2 *
.xo .ox .xx&#x ♦ 0 4 4 | 0 0 0 2 2 8 2 2 | 0 0 0 0 0 0 1 4 4 4 1 | 0 0 0 0 0 0 0 2 2 2 | * * * * 1

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