Acronym pabdimo, dot||scad||dot
Name parabidiminished mo,
dodecateron atop pseudo small cellated dodecateron atop dodecateron
Circumradius 1
Lace city
in approx. ASCII-art
   r     R   		-- o3o3x3o3o (dot)
             
P     S     p		-- x3o3o3o3x (scad)
             
   r     R   		-- o3o3x3o3o (dot)

where:
r = o3x3o3o (rap)
R = o3o3x3o (inv. rap)
p = x3o3o3o (pen)
P = o3o3o3x (dual pen)
S = x3o3o3x (spid)
o   A   V   o	-- o3o3x3o3o (dot)
             
  V   +   A  	-- x3o3o3o3x (scad)
             
o   A   V   o	-- o3o3x3o3o (dot)

where:
o =  o3o   o3o      (point)
A =  x3o   x3o      (triddip)
V =  o3x   o3x      (bi-inv. triddip)
+ = xo3xo ox3ox&#zq (bihexagonal tegum)
a     O     b		-- o3o3x3o3o (dot)
             
B     c     A		-- x3o3o3o3x (scad)
             
a     O     b		-- o3o3x3o3o (dot)

|           +-- x3o3o *b3o3o (hin)
+-------------- o3o3x *b3o3o (alt. hin)

where:
a = x3o3o o (tet)
b = o3o3x o (dual tet)
A = x3o3o x (tepe)
B = o3o3x x (inv. tepe)
O = o3x3o x (ope)
c = compound of
    x3o3x o (co)
    o3o3o u (ortho u-line)
Confer
uniform relative:
mo   dotip  
related segmentopeta:
dottascad  

This polypeton well can be considered to be some augmentation of dotip, thereby reusing both bases of this tower. And the vertices of the equatorial layer (scad) happen to be atop the ope ridges of that prism.


Incidence matrix according to Dynkin symbol

oxo3ooo3xox3ooo3oxo&#x   → both heights = 1/2
(dot || (pseudo) scad || dot)

o..3o..3o..3o..3o..    & | 40  * |   9   9   0 |  18  18  36   0  0 |  6  9   6  36   9  36  0   0 |  6  12   6  18   9  9  0  0  0 | 1  6  6  1
.o.3.o.3.o.3.o.3.o.      |  * 30 |   0  12   8 |   0  48  24  12 12 |  0  0  24  48  48  16  8  24 |  0  16  48  16  24  2  2  8  6 | 0  4 16 12
-------------------------+-------+-------------+--------------------+------------------------------+--------------------------------+-----------
... ... x.. ... ...    & |  2  0 | 180   *   * |   4   0   4   0  0 |  2  4   0   4   0   8  0   0 |  4   4   0   4   1  4  0  0  0 | 1  4  2  0
oo.3oo.3oo.3oo.3oo.&#x & |  1  1 |   * 360   * |   0   4   4   0  0 |  0  0   2   8   4   4  0   0 |  0   4   4   4   4  1  0  0  0 | 0  2  4  1
.x. ... ... ... ...    & |  0  2 |   *   * 120 |   0   6   0   3  3 |  0  0   6   6  12   0  3   9 |  0   6  18   2   6  0  1  4  3 | 0  2  8  6
-------------------------+-------+-------------+--------------------+------------------------------+--------------------------------+-----------
... o..3x.. ... ...    & |  3  0 |   3   0   0 | 240   *   *   *  * |  1  2   0   0   0   2  0   0 |  3   2   0   1   0  2  0  0  0 | 1  3  1  0
ox. ... ... ... ...&#x & |  1  2 |   0   2   1 |   * 720   *   *  * |  0  0   1   2   2   0  0   0 |  0   2   3   1   2  0  0  0  0 | 0  1  3  1
... ... xo. ... ...&#x & |  2  1 |   1   2   0 |   *   * 720   *  * |  0  0   0   2   0   2  0   0 |  0   2   0   2   1  1  0  0  0 | 0  2  2  0
.x.3.o. ... ... ...    & |  0  3 |   0   0   3 |   *   *   * 120  * |  0  0   2   0   0   0  2   2 |  0   4   4   0   0  0  1  2  1 | 0  2  4  2
.x. ... ... ... .x.      |  0  4 |   0   0   4 |   *   *   *   * 90 |  0  0   0   0   4   0  0   4 |  0   0   8   0   2  0  0  2  2 | 0  0  4  4
-------------------------+-------+-------------+--------------------+------------------------------+--------------------------------+-----------
o..3o..3x.. ... ...    &   4  0 |   6   0   0 |   4   0   0   0  0 | 60  *   *   *   *   *  *   * |  2   2   0   0   0  0  0  0  0 | 1  2  1  0
... o..3x..3o.. ...    &   6  0 |  12   0   0 |   8   0   0   0  0 |  * 60   *   *   *   *  *   * |  2   0   0   0   0  1  0  0  0 | 1  2  0  0
ox.3oo. ... ... ...&#x &   1  3 |   0   3   3 |   0   3   0   1  0 |  *  * 240   *   *   *  *   * |  0   2   2   0   0  0  0  0  0 | 0  1  2  1
ox. ... xo. ... ...&#x &   2  2 |   1   4   1 |   0   2   2   0  0 |  *  *   * 720   *   *  *   * |  0   1   0   1   1  0  0  0  0 | 0  1  2  0
ox. ... ... ... ox.&#x &   1  4 |   0   4   4 |   0   4   0   0  1 |  *  *   *   * 360   *  *   * |  0   0   2   0   1  0  0  0  0 | 0  0  2  1
... oo.3xo. ... ...&#x &   3  1 |   3   3   0 |   1   0   3   0  0 |  *  *   *   *   * 480  *   * |  0   1   0   1   0  1  0  0  0 | 0  2  1  0
.x.3.o.3.o. ... ...    &   0  4 |   0   0   6 |   0   0   0   4  0 |  *  *   *   *   *   * 60   * |  0   2   0   0   0  0  1  1  0 | 0  2  2  0
.x.3.o. ... ... .x.    &   0  6 |   0   0   9 |   0   0   0   2  3 |  *  *   *   *   *   *  * 120 |  0   0   2   0   0  0  0  1  1 | 0  0  2  2
-------------------------+-------+-------------+--------------------+------------------------------+--------------------------------+-----------
o..3o..3x..3o.. ...    &  10  0 |  30   0   0 |  30   0   0   0  0 |  5  5   0   0   0   0  0   0 | 24   *   *   *   *  *  *  *  * | 1  1  0  0
ox.3oo.3xo. ... ...&#x &   4  4 |   6  12   6 |   4  12  12   4  0 |  1  0   4   6   0   4  1   0 |  * 120   *   *   *  *  *  *  * | 0  1  1  0
ox.3oo. ... ... ox.&#x &   1  6 |   0   6   9 |   0   9   0   2  3 |  0  0   2   0   3   0  0   1 |  *   * 240   *   *  *  *  *  * | 0  0  1  1
ox. ... xo.3oo. ...&#x &   3  2 |   3   6   1 |   1   3   6   0  0 |  0  0   0   3   0   2  0   0 |  *   *   * 240   *  *  *  *  * | 0  1  1  0
ox. ... xo. ... ox.&#x &   2  4 |   1   8   4 |   0   8   4   0  1 |  0  0   0   4   2   0  0   0 |  *   *   *   * 180  *  *  *  * | 0  0  2  0
... oo.3xo.3oo. ...&#x &   6  1 |  12   6   0 |   8   0  12   0  0 |  0  1   0   0   0   8  0   0 |  *   *   *   *   * 60  *  *  * | 0  2  0  0
.x.3.o.3.o.3.o. ...    &   0  5 |   0   0  10 |   0   0   0  10  0 |  0  0   0   0   0   0  5   0 |  *   *   *   *   *  * 12  *  * | 0  2  0  0
.x.3.o.3.o. ... .x.    &   0  8 |   0   0  16 |   0   0   0   8  6 |  0  0   0   0   0   0  2   4 |  *   *   *   *   *  *  * 30  * | 0  0  2  0
.x.3.o. ... .o.3.x.        0  9 |   0   0  18 |   0   0   0   6  9 |  0  0   0   0   0   0  0   6 |  *   *   *   *   *  *  *  * 20 | 0  0  0  2
-------------------------+-------+-------------+--------------------+------------------------------+--------------------------------+-----------
o..3o..3x..3o..3o..    &  20  0 |  90   0   0 | 120   0   0   0  0 | 30 30   0   0   0   0  0   0 | 12   0   0   0   0  0  0  0  0 | 2  *  *  *
ox.3oo.3xo.3oo. ...&#x &  10  5 |  30  30  10 |  30  30  60  10  0 |  5  5  10  30   0  40  5   0 |  1   5   0  10   0  5  1  0  0 | * 24  *  *
ox.3oo.3xo. ... ox.&#x &   4  8 |   6  24  16 |   4  36  24   8  6 |  1  0   8  24  12   8  2   4 |  0   2   4   4   6  0  0  1  0 | *  * 60  *
ox.3oo. ... oo.3ox.&#x &   1  9 |   0   9  18 |   0  18   0   6  9 |  0  0   6   0   9   0  0   6 |  0   0   6   0   0  0  0  0  1 | *  *  * 40

© 2004-2019
top of page