Acronym gyetac
Name gyroelongated triacontaditeron
Circumradius ...
Lace city
in approx. ASCII-art 
    o        	where:
        T    	T = x3o3o (tet)
o   O       o	t = o3o3x (dual tet)
        t    	O = o3x3o (oct)
    o        	o = o3o3o (point)

|   |   |   +	o3o3o *b3o (point)
|   |   +----	x3o3o *b3o (hex)
|   +--------	o3o3o *b3x (gyro hex)
+------------	o3o3o *b3o (point)
Dihedral angles
  • at tet between pen and hex:   arccos[-2/sqrt(5)] = 153.434949°
  • at tet between pen and tete:   arccos(-3/5) = 126.869898°
  • at tet between hex and tete:   arccos[-1/sqrt(5)] = 116.565051°
  • at tet between hex and hex:   90°
Face vector 18, 96, 208, 168, 40
Confer
segmentotera:
hexpy  
related CRFs:
5D Dutour polyteron type A   pexgyetac   pabgysiphin   pabex gyetac  
uniform relative:
hin   tac  

This polyteron is nothing but an external blend of hin and 2 antipodal hexpies, adjoining at an hex. There it just happens that the dihedral angle between some of the pens becomes flat, i.e. they join into a tete each.

This CRF also occurs as partial Stott contraction of pabgysiphin.


Incidence matrix according to Dynkin symbol

oxoo3oooo3ooxo *b3oooo&#xt   → all heights = 1/sqrt(2) = 0.707107
(pt || hex || gyro hex || pt)

o...3o...3o... *b3o...     & | 2  * ♦  8  0  0 | 24  0  0 | 32  0  0  0 |  8  8 0
.o..3.o..3.o.. *b3.o..     & | * 16 |  1  6  4 |  6 12 18 | 12  4 16  6 |  4  5 4
-----------------------------+------+----------+----------+-------------+--------
oo..3oo..3oo.. *b3oo..&#x  & | 1  1 | 16  *  * ♦  6  0  0 | 12  0  0  0 |  4  4 0
.x.. .... ....    ....     & | 0  2 |  * 48  * |  1  4  2 |  4  2  4  1 |  2  2 2
.oo.3.oo.3.oo. *b3.oo.&#x    | 0  2 |  *  * 32 ♦  0  0  6 |  0  0  6  3 |  0  2 3
-----------------------------+------+----------+----------+-------------+--------
ox.. .... ....    ....&#x  & | 1  2 |  2  1  0 | 48  *  * |  4  0  0  0 |  2  2 0
.x..3.o.. ....    ....     & | 0  3 |  0  3  0 |  * 64  * |  1  1  1  0 |  1  1 1
.xo. .... ....    ....&#x  & | 0  3 |  0  1  2 |  *  * 96 |  0  0  2  1 |  0  1 2
-----------------------------+------+----------+----------+-------------+--------
ox..3oo.. ....    ....&#x  & ♦ 1  3 |  3  3  0 |  3  1  0 | 64  *  *  * |  1  1 0
.x..3.o..3.o..    ....     & ♦ 0  4 |  0  6  0 |  0  4  0 |  * 16  *  * |  1  0 1
.xo.3.oo. ....    ....&#x  & ♦ 0  4 |  0  3  3 |  0  1  3 |  *  * 64  * |  0  1 1
.xo. .... .ox.    ....&#x    ♦ 0  4 |  0  2  4 |  0  0  4 |  *  *  * 24 |  0  0 2
-----------------------------+------+----------+----------+-------------+--------
ox..3oo..3oo..    ....&#x  & ♦ 1  4 |  4  6  0 |  6  4  0 |  4  1  0  0 | 16  * *
oxo.3ooo. .... *b3ooo.&#xt & ♦ 1  5 |  4  6  4 |  6  4  6 |  4  0  4  0 |  * 16 *
.xo.3.oo.3.ox.    ....&#x    ♦ 0  8 |  0 12 12 |  0  8 24 |  0  2  8  6 |  *  * 8

© 2004-2024
top of page