Acronym aubautipip
Name augmented biaugmented-triangular-prism prism
Coordinates
  1. (1/2, 1/2, 0, 1/sqrt(3))                & all changes of sign in first 3 coords.
    (biaugmentation rim)
  2. (1/2, 0, A/2, A/sqrt(12))             & all changes of sign in first 3 coords.
    (augmentation wedges)
  3. (1/2, 1/2, 1/2, -1/sqrt(12))          & all changes of sign in first 3 coords.
    (pseudo cube)
  4. (0, 0, 0, -B/sqrt(3))
    (opposite apex)
where A = (1+sqrt(6))/2 = 1.724745, B = (1+sqrt(3))/2 = 1.366025
Dihedral angles
  • at {4} between trip and trip (across iso-biaugmentation rim):   arccos[-(1+2 sqrt(6))/6] = 169.471221°
  • at {4} between squippy and trip (across aniso-biaugmentation rim):   arccos[(1-sqrt(2)-sqrt(3)-sqrt(6))/sqrt(24)] = 159.735610°
  • at {4} between trip and trip (across wedge-augmentation rim):   arccos[-sqrt(2/3)] = 144.735610°
  • at {4} between bautip and squippy:   135°
  • at {4} between squippy and trip (across pyramid-augmentation rim):   135°
  • at {4} between trip and trip (within squippyp-part):   arccos(-1/3) = 109.471221°
  • at {3} between bautip and trip:   90°
Confer
uniform relative:
tisdip  
blend-component:
cubpy   squippyp   tisdip  
related segmentochora:
cubpy   squippyp  
related CRFs:
autipip   bautipip  

Incidence matrix according to Dynkin symbol

xxxo xoxo oAxo&#xt   → height(1,2) = (3-sqrt(6))/sqrt(48) = 0.079459
                       height(2,3) = (3+sqrt(6))/sqrt(48) = 0.786566
                       height(3,4) = 1/2
                       where A = (1+sqrt(6))/2 = 1.724745
(square || (pseudo) (x,A)-rectangle || (pseudo) cube || point)

o... o... o...     | 4 * * * | 1 1 2 2 0 0 0 0 0 0 | 1 2 2 2 2 1 0 0 0 0 0 0 0 0 | 2 2 1 1 0 0 0 0
.o.. .o.. .o..     | * 4 * * | 0 0 2 0 1 2 0 0 0 0 | 0 2 1 2 0 0 2 1 0 0 0 0 0 0 | 1 2 1 0 1 0 0 0
..o. ..o. ..o.     | * * 8 * | 0 0 0 1 0 1 1 1 1 1 | 0 0 0 1 1 1 1 1 1 1 1 1 1 1 | 0 1 1 1 1 1 1 1
...o ...o ...o     | * * * 1  0 0 0 0 0 0 0 0 0 8 | 0 0 0 0 0 0 0 0 0 0 0 4 4 4 | 0 0 0 0 0 2 2 2
-------------------+---------+---------------------+-----------------------------+----------------
x... .... ....     | 2 0 0 0 | 2 * * * * * * * * * | 1 2 0 0 2 0 0 0 0 0 0 0 0 0 | 2 2 0 1 0 0 0 0
.... x... ....     | 2 0 0 0 | * 2 * * * * * * * * | 1 0 2 0 0 0 0 0 0 0 0 0 0 0 | 2 0 1 0 0 0 0 0
oo.. oo.. oo..&#x  | 1 1 0 0 | * * 8 * * * * * * * | 0 1 1 1 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 0
o.o. o.o. o.o.&#x  | 1 0 1 0 | * * * 8 * * * * * * | 0 0 0 1 1 1 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 0
.x.. .... ....     | 0 2 0 0 | * * * * 2 * * * * * | 0 2 0 0 0 0 2 0 0 0 0 0 0 0 | 1 1 0 0 1 0 0 0
.oo. .oo. .oo.&#x  | 0 1 1 0 | * * * * * 8 * * * * | 0 0 0 1 0 0 1 1 0 0 0 0 0 0 | 0 1 1 0 1 0 0 0
..x. .... ....     | 0 0 2 0 | * * * * * * 4 * * * | 0 0 0 0 1 0 1 0 1 1 0 1 0 0 | 0 1 0 1 1 1 1 0
.... ..x. ....     | 0 0 2 0 | * * * * * * * 4 * * | 0 0 0 0 0 0 0 1 1 0 1 0 1 0 | 0 0 1 0 1 1 0 1
.... .... ..x.     | 0 0 2 0 | * * * * * * * * 4 * | 0 0 0 0 0 1 0 0 0 1 1 0 0 1 | 0 0 1 1 0 0 1 1
..oo ..oo ..oo&#x  | 0 0 1 1 | * * * * * * * * * 8 | 0 0 0 0 0 0 0 0 0 0 0 1 1 1 | 0 0 0 0 0 1 1 1
-------------------+---------+---------------------+-----------------------------+----------------
x... x... ....     | 4 0 0 0 | 2 2 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * * | 2 0 0 0 0 0 0 0
xx.. .... ....&#x  | 2 2 0 0 | 1 0 2 0 1 0 0 0 0 0 | * 4 * * * * * * * * * * * * | 1 1 0 0 0 0 0 0
.... xo.. ....&#x  | 2 1 0 0 | 0 1 2 0 0 0 0 0 0 0 | * * 4 * * * * * * * * * * * | 1 0 1 0 0 0 0 0
ooo. ooo. ooo.&#x  | 1 1 1 0 | 0 0 1 1 0 1 0 0 0 0 | * * * 8 * * * * * * * * * * | 0 1 1 0 0 0 0 0
x.x. .... ....&#x  | 2 0 2 0 | 1 0 0 2 0 0 1 0 0 0 | * * * * 4 * * * * * * * * * | 0 1 0 1 0 0 0 0
.... .... o.x.&#x  | 1 0 2 0 | 0 0 0 2 0 0 0 0 1 0 | * * * * * 4 * * * * * * * * | 0 0 1 1 0 0 0 0
.xx. .... ....&#x  | 0 2 2 0 | 0 0 0 0 1 2 1 0 0 0 | * * * * * * 4 * * * * * * * | 0 1 0 0 1 0 0 0
.... .ox. ....&#x  | 0 1 2 0 | 0 0 0 0 0 2 0 1 0 0 | * * * * * * * 4 * * * * * * | 0 0 1 0 1 0 0 0
..x. ..x. ....     | 0 0 4 0 | 0 0 0 0 0 0 2 2 0 0 | * * * * * * * * 2 * * * * * | 0 0 0 0 1 1 0 0
..x. .... ..x.     | 0 0 4 0 | 0 0 0 0 0 0 2 0 2 0 | * * * * * * * * * 2 * * * * | 0 0 0 1 0 0 1 0
.... ..x. ..x.     | 0 0 4 0 | 0 0 0 0 0 0 0 2 2 0 | * * * * * * * * * * 2 * * * | 0 0 1 0 0 0 0 1
..xo .... ....&#x  | 0 0 2 1 | 0 0 0 0 0 0 1 0 0 2 | * * * * * * * * * * * 4 * * | 0 0 0 0 0 1 1 0
.... ..xo ....&#x  | 0 0 2 1 | 0 0 0 0 0 0 0 1 0 2 | * * * * * * * * * * * * 4 * | 0 0 0 0 0 1 0 1
.... .... ..xo&#x  | 0 0 2 1 | 0 0 0 0 0 0 0 0 1 2 | * * * * * * * * * * * * * 4 | 0 0 0 0 0 0 1 1
-------------------+---------+---------------------+-----------------------------+----------------
xx.. xo.. ....&#x   4 2 0 0 | 2 2 4 0 1 0 0 0 0 0 | 1 2 2 0 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * *
xxx. .... ....&#x   2 2 2 0 | 1 0 2 2 1 2 1 0 0 0 | 0 1 0 2 1 0 1 0 0 0 0 0 0 0 | * 4 * * * * * *
.... xox. oAx.&#xt  2 2 4 0 | 0 1 4 4 0 4 0 2 2 0 | 0 0 2 4 0 2 0 2 0 0 1 0 0 0 | * * 2 * * * * *
x.x. .... o.x.&#x   2 0 4 0 | 1 0 0 4 0 0 2 0 2 0 | 0 0 0 0 2 2 0 0 0 1 0 0 0 0 | * * * 2 * * * *
.xx. .ox. ....&#x   0 2 4 0 | 0 0 0 0 1 4 2 2 0 0 | 0 0 0 0 0 0 2 2 1 0 0 0 0 0 | * * * * 2 * * *
..xo ..xo ....&#x   0 0 4 1 | 0 0 0 0 0 0 2 2 0 4 | 0 0 0 0 0 0 0 0 1 0 0 2 2 0 | * * * * * 2 * *
..xo .... ..xo&#x   0 0 4 1 | 0 0 0 0 0 0 2 0 2 4 | 0 0 0 0 0 0 0 0 0 1 0 2 0 2 | * * * * * * 2 *
.... ..xo ..xo&#x   0 0 4 1 | 0 0 0 0 0 0 0 2 2 4 | 0 0 0 0 0 0 0 0 0 0 1 0 2 2 | * * * * * * * 2

© 2004-2018
top of page