Acronym bauautipip
Name biaugmented augmented-triangular-prism prism
Circumradius ...
Coordinates
  1. (1/2, 0, 0, 1/sqrt(2))                            & all changes of sign in 1st coord.
    (top line)
  2. (1/2, 1/2, 1/2, 0)                                 & all changes of sign
    (joining cube)
  3. (0, 0, (1+sqrt(3))/4, -(1+sqrt(3))/4)     & all changes of sign in 3rd coord.
    (augmentation apices)
  4. (1/2, 1/2, 0, -sqrt(3)/2)                       & all changes of sign in 1st & 2nd coord.
    (bottom square)
Dihedral angles
  • at {4} (type 4d) between squippy and trip:   arccos[(1-sqrt(2)-sqrt(3)-sqrt(6))/sqrt(24)] = 159.735610°
  • at {4} (type 4a) between squippy and squippy:   150°
  • at {4} (type 4e) between trip and trip:   arccos[-sqrt(2/3)] = 144.735610°
  • at {4} (type 4c) between autip and squippy:   135°
  • at {4} (type 4b) between squippy and trip:   135°
  • at {3} between squippy and squippy:   120°
  • at {4} (type 4f) between trip and trip:   arccos(-1/3) = 109.471221°
  • at {3} between autip and trip:   90°
Face vector 16, 49, 53, 20
Confer
uniform relative:
tisdip  
blend-component:
cubpy   squippyp   tisdip  
related segmentochora:
cubpy   squippyp  
related CRFs:
autipip  

Incidence matrix according to Dynkin symbol

xoxx xoxo oAxo&#xt   → height(1,2) = (2 sqrt(2)-1-sqrt(3))/4 = 0.024094
                       height(2,3) = (1+sqrt(3))/4 = 0.683013 
                       height(3,4) = sqrt(3)/2 = 0.866025
                       where A = (1+sqrt(3))/2 = 1.366025
({4} || (pseudo) perp line || (pseudo) cube || para line)

o... o... o...     | 4 * * * | 1 1 2 2 0 0 0 0 0 0 | 1 2 2 2 2 1 2 0 0 0 0 0 0 0 | 2 1 1 2 2 0 0 0
.o.. .o.. .o..     | * 2 * * ♦ 0 0 4 0 4 0 0 0 0 0 | 0 2 2 0 0 0 4 2 2 0 0 0 0 0 | 1 0 0 2 2 1 0 0
..o. ..o. ..o.     | * * 8 * | 0 0 0 1 1 1 1 1 1 0 | 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     | * * * 2 | 0 0 0 0 0 0 0 0 4 1 | 0 0 0 0 0 0 0 0 0 0 0 4 2 2 | 0 0 1 0 0 0 2 2
-------------------+---------+---------------------+-----------------------------+----------------
x... .... ....     | 2 0 0 0 | 2 * * * * * * * * * | 1 2 0 2 0 0 0 0 0 0 0 0 0 0 | 2 1 0 2 0 0 0 0
.... x... ....     | 2 0 0 0 | * 2 * * * * * * * * | 1 0 2 0 2 0 0 0 0 0 0 0 0 0 | 2 0 1 0 2 0 0 0
oo.. oo.. oo..&#x  | 1 1 0 0 | * * 8 * * * * * * * | 0 1 1 0 0 0 1 0 0 0 0 0 0 0 | 1 0 0 1 1 0 0 0
o.o. o.o. o.o.&#x  | 1 0 1 0 | * * * 8 * * * * * * | 0 0 0 1 1 1 1 0 0 0 0 0 0 0 | 0 1 1 1 1 0 0 0
.oo. .oo. .oo.&#x  | 0 1 1 0 | * * * * 8 * * * * * | 0 0 0 0 0 0 1 1 1 0 0 0 0 0 | 0 0 0 1 1 1 0 0
..x. .... ....     | 0 0 2 0 | * * * * * 4 * * * * | 0 0 0 1 0 0 0 1 0 1 1 1 0 0 | 0 1 0 1 0 1 1 1
.... ..x. ....     | 0 0 2 0 | * * * * * * 4 * * * | 0 0 0 0 1 0 0 0 1 1 0 0 1 0 | 0 0 1 0 1 1 1 0
.... .... ..x.     | 0 0 2 0 | * * * * * * * 4 * * | 0 0 0 0 0 1 0 0 0 0 1 0 0 1 | 0 1 1 0 0 0 0 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 1 0 0 0 1 1
...x .... ....     | 0 0 0 2 | * * * * * * * * * 1 | 0 0 0 0 0 0 0 0 0 0 0 4 0 0 | 0 0 0 0 0 0 2 2
-------------------+---------+---------------------+-----------------------------+----------------
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  4a
xo.. .... ....&#x  | 2 1 0 0 | 1 0 2 0 0 0 0 0 0 0 | * 4 * * * * * * * * * * * * | 1 0 0 1 0 0 0 0
.... xo.. ....&#x  | 2 1 0 0 | 0 1 2 0 0 0 0 0 0 0 | * * 4 * * * * * * * * * * * | 1 0 0 0 1 0 0 0
x.x. .... ....&#x  | 2 0 2 0 | 1 0 0 2 0 1 0 0 0 0 | * * * 4 * * * * * * * * * * | 0 1 0 1 0 0 0 0  4b
.... x.x. ....&#x  | 2 0 2 0 | 0 1 0 2 0 0 1 0 0 0 | * * * * 4 * * * * * * * * * | 0 0 1 0 1 0 0 0  4c
.... .... o.x.&#x  | 1 0 2 0 | 0 0 0 2 0 0 0 1 0 0 | * * * * * 4 * * * * * * * * | 0 1 1 0 0 0 0 0
ooo. ooo. ooo.&#x  | 1 1 1 0 | 0 0 1 1 1 0 0 0 0 0 | * * * * * * 8 * * * * * * * | 0 0 0 1 1 0 0 0
.ox. .... ....&#x  | 0 1 2 0 | 0 0 0 0 2 1 0 0 0 0 | * * * * * * * 4 * * * * * * | 0 0 0 1 0 1 0 0
.... .ox. ....&#x  | 0 1 2 0 | 0 0 0 0 2 0 1 0 0 0 | * * * * * * * * 4 * * * * * | 0 0 0 0 1 1 0 0
..x. ..x. ....     | 0 0 4 0 | 0 0 0 0 0 2 2 0 0 0 | * * * * * * * * * 2 * * * * | 0 0 0 0 0 1 1 0  4d
..x. .... ..x.     | 0 0 4 0 | 0 0 0 0 0 2 0 2 0 0 | * * * * * * * * * * 2 * * * | 0 1 0 0 0 0 0 1  4e
..xx .... ....&#x  | 0 0 2 2 | 0 0 0 0 0 1 0 0 2 1 | * * * * * * * * * * * 4 * * | 0 0 0 0 0 0 1 1  4f
.... ..xo ....&#x  | 0 0 2 1 | 0 0 0 0 0 0 1 0 2 0 | * * * * * * * * * * * * 4 * | 0 0 1 0 0 0 1 0
.... .... ..xo&#x  | 0 0 2 1 | 0 0 0 0 0 0 0 1 2 0 | * * * * * * * * * * * * * 4 | 0 0 1 0 0 0 0 1
-------------------+---------+---------------------+-----------------------------+----------------
xo.. xo.. ....&#x  ♦ 4 1 0 0 | 2 2 4 0 0 0 0 0 0 0 | 1 2 2 0 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * *
x.x. .... o.x.&#x  ♦ 2 0 4 0 | 1 0 0 4 0 2 0 2 0 0 | 0 0 0 2 0 2 0 0 0 0 1 0 0 0 | * 2 * * * * * *
.... x.xo o.xo&#xt ♦ 2 0 4 1 | 0 1 0 4 0 0 2 2 4 0 | 0 0 0 0 2 2 0 0 0 0 0 0 2 2 | * * 2 * * * * *
xox. .... ....&#x  ♦ 2 1 2 0 | 1 0 2 2 2 1 0 0 0 0 | 0 1 0 1 0 0 2 1 0 0 0 0 0 0 | * * * 4 * * * *
.... xox. ....&#x  ♦ 2 1 2 0 | 0 1 2 2 2 0 1 0 0 0 | 0 0 1 0 1 0 2 0 1 0 0 0 0 0 | * * * * 4 * * *
.ox. .ox. ....&#x  ♦ 0 1 4 0 | 0 0 0 0 4 2 2 0 0 0 | 0 0 0 0 0 0 0 2 2 1 0 0 0 0 | * * * * * 2 * *
..xx ..xo ....&#x  ♦ 0 0 4 2 | 0 0 0 0 0 2 2 0 4 1 | 0 0 0 0 0 0 0 0 0 1 0 2 2 0 | * * * * * * 2 *
..xx .... ..xo&#x  ♦ 0 0 4 2 | 0 0 0 0 0 2 0 2 4 1 | 0 0 0 0 0 0 0 0 0 0 1 2 0 2 | * * * * * * * 2

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