autipip

Acronym	autipip
Name	augmented-triangular-prism prism
Circumradius	...
Coordinates	(1/2, 0, 0, 1/sqrt(2)) & all changes of sign in 1^st coord. (top line) (1/2, 1/2, 1/2, 0) & all changes of sign (joining cube) (1/2, 1/2, 0, -sqrt(3)/2) & all changes of sign in 1^st & 2^nd coord. (bottom square)
Dihedral angles	at {4} between trip and trip (across augmentation rim): arccos[-sqrt(2/3)] = 144.735610° at {4} between cube and trip (across augmentation rim): arccos[-(sqrt(6)-1)/sqrt(12)] = 114.735610° at {4} between trip and trip (within squippyp-part): arccos(-1/3) = 109.471221° at {4} between autip and cube: 90° at {4} between cube and trip (within tisdip-part): 90° at {3} between autip and trip: 90° at {4} between cube and cube: 60°
Face vector	14, 33, 29, 10
Confer	uniform relative: tisdip blend-component: tisdip squippyp related segmentochora: squippyp related CRFs: bauautipip aubautipip tautipip gyautisdip general polytopal classes: bistratic lace towers

Incidence matrix according to Dynkin symbol

xxx xxo oxo&#xt   → height(1,2) = 1/sqrt(2) = 0.707107
                    height(2,3) = sqrt(3)/2 = 0.866025
({4} || (pseudo) cube || line)

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

top of page