tetacoa cube

Acronym	tetacoa cube
Name	tetrahedron atop cuboctahedron atop cube
Circumradius	...
Lace city in approx. ASCII-art	x o o x -- x3o3o (tet) x x ou uo x x -- x3o3x (co) (qo oq) (oq qo) -- qo3oo3oq&#zx (cube)
Dihedral angles	at {3} between tet and tet (across rim): arccos[-(3-sqrt(8)+sqrt[90 sqrt(8)-135])/sqrt(128)] = 169.000195° at {3} between tet and trip (across rim): arccos[-(3-sqrt(8)+sqrt[30 sqrt(8)-45])/sqrt(48)] = 159.382864° at {4} between squap and trip (across rim): arccos[-(1-sqrt(2)+sqrt[20 sqrt(2)-15])/sqrt(12 sqrt(2))] = 141.646907° at {4} between trip and trip (in tetaco): arccos(-2/3) = 131.810315° at {3} between tet and trip (in tetaco): arccos(-sqrt(3/8)) = 127.761244° at {3} between squap and tet (in cubaco): arccos[-(sqrt(8)-1)/sqrt(sqrt(128))] = 122.928678° at {4} between cube and squap (in cubaco): arccos[-(sqrt(2)-1)/sqrt(sqrt(8))] = 104.258250° at {3} between squap and squap (in cubaco): arccos[-(3-sqrt(8))/sqrt(8)] = 93.477707°
Face vector	24, 78, 84, 30
Confer	related segmentochora: tet \|\| co cube \|\| co general polytopal classes: bistratic lace towers

This CRF polychoron, if considered as ooo3oxo4sox&#xt, is to be understood as an alternation within the first layer only. However, that very snubbing then alternates the triangles of the medial layer and the vertices of the bottom layer in the same run, although those are both being kept each.

Incidence matrix according to Dynkin symbol

xx(oq)3oo(oo)3ox(qo)&#xt   → height(1,2) = sqrt(5/8) = 0.790569
                             height(2,3) = sqrt[sqrt(2)-3/4] = 0.814993
(tet || co || cube)

o.(..)3o.(..)3o.(..)     | 4  * * * ♦ 3  3  0  0  0  0  0 | 3  6  3 0 0 0  0  0  0 0 | 1 3 3 1 0 0 0 0
.o(..)3.o(..)3.o(..)     | * 12 * * | 0  1  2  2  1  1  0 | 0  2  2 1 2 1  2  2  1 0 | 0 1 2 1 1 1 2 0
..(o.)3..(o.)3..(o.)     | *  * 4 * | 0  0  0  0  3  0  3 | 0  0  0 0 0 0  3  0  3 3 | 0 0 0 0 1 0 3 1
..(.o)3..(.o)3..(.o)     | *  * * 4 | 0  0  0  0  0  3  3 | 0  0  0 0 0 0  0  3  3 3 | 0 0 0 0 0 1 3 1
-------------------------+----------+---------------------+--------------------------+----------------
x.(..) ..(..) ..(..)     | 2  0 0 0 | 6  *  *  *  *  *  * | 2  2  0 0 0 0  0  0  0 0 | 1 2 1 0 0 0 0 0
oo(..)3oo(..)3oo(..)&#x  | 1  1 0 0 | * 12  *  *  *  *  * | 0  2  2 0 0 0  0  0  0 0 | 0 1 2 1 0 0 0 0
.x(..) ..(..) ..(..)     | 0  2 0 0 | *  * 12  *  *  *  * | 0  1  0 1 1 0  1  0  0 0 | 0 1 1 0 1 0 1 0
..(..) ..(..) .x(..)     | 0  2 0 0 | *  *  * 12  *  *  * | 0  0  1 0 1 1  0  1  0 0 | 0 0 1 1 0 1 1 0
.o(o.)3.o(o.)3.o(o.)&#x  | 0  1 1 0 | *  *  *  * 12  *  * | 0  0  0 0 0 0  2  0  1 0 | 0 0 0 0 1 0 2 0
.o(.o)3.o(.o)3.o(.o)&#x  | 0  1 0 1 | *  *  *  *  * 12  * | 0  0  0 0 0 0  0  2  1 0 | 0 0 0 0 0 1 2 0
..(oo)3..(oo)3..(oo)&#x  | 0  0 1 1 | *  *  *  *  *  * 12 | 0  0  0 0 0 0  0  0  1 2 | 0 0 0 0 0 0 2 1
-------------------------+----------+---------------------+--------------------------+----------------
x.(..)3o.(..) ..(..)     | 3  0 0 0 | 3  0  0  0  0  0  0 | 4  *  * * * *  *  *  * * | 1 1 0 0 0 0 0 0
xx(..) ..(..) ..(..)&#x  | 2  2 0 0 | 1  2  1  0  0  0  0 | * 12  * * * *  *  *  * * | 0 1 1 0 0 0 0 0
..(..) ..(..) ox(..)&#x  | 1  2 0 0 | 0  2  0  1  0  0  0 | *  * 12 * * *  *  *  * * | 0 0 1 1 0 0 0 0
.x(..)3.o(..) ..(..)     | 0  3 0 0 | 0  0  3  0  0  0  0 | *  *  * 4 * *  *  *  * * | 0 1 0 0 1 0 0 0
.x(..) ..(..) .x(..)     | 0  4 0 0 | 0  0  2  2  0  0  0 | *  *  * * 6 *  *  *  * * | 0 0 1 0 0 0 1 0
..(..) .o(..)3.x(..)     | 0  3 0 0 | 0  0  0  3  0  0  0 | *  *  * * * 4  *  *  * * | 0 0 0 1 0 1 0 0
.x(o.) ..(..) ..(..)&#x  | 0  2 1 0 | 0  0  1  0  2  0  0 | *  *  * * * * 12  *  * * | 0 0 0 0 1 0 1 0
..(..) ..(..) .x(.o)&#x  | 0  2 0 1 | 0  0  0  1  0  2  0 | *  *  * * * *  * 12  * * | 0 0 0 0 0 1 1 0
.o(oo)3.o(oo)3.o(oo)&#x  | 0  1 1 1 | 0  0  0  0  1  1  1 | *  *  * * * *  *  * 12 * | 0 0 0 0 0 0 2 0
..(oq) ..(..) ..(qo)&#zx | 0  0 2 2 | 0  0  0  0  0  0  4 | *  *  * * * *  *  *  * 6 | 0 0 0 0 0 0 1 1
-------------------------+----------+---------------------+--------------------------+----------------
x.(..)3o.(..)3o.(..)     ♦ 4  0 0 0 | 6  0  0  0  0  0  0 | 4  0  0 0 0 0  0  0  0 0 | 1 * * * * * * *
xx(..)3oo(..) ..(..)&#x  ♦ 3  3 0 0 | 3  3  3  0  0  0  0 | 1  3  0 1 0 0  0  0  0 0 | * 4 * * * * * *
xx(..) ..(..) ox(..)&#x  ♦ 2  4 0 0 | 1  4  2  2  0  0  0 | 0  2  2 0 1 0  0  0  0 0 | * * 6 * * * * *
..(..) oo(..)3ox(..)&#x  ♦ 1  3 0 0 | 0  3  0  3  0  0  0 | 0  0  3 0 0 1  0  0  0 0 | * * * 4 * * * *
.x(o.)3.o(o.) ..(..)&#x  ♦ 0  3 1 0 | 0  0  3  0  3  0  0 | 0  0  0 1 0 0  3  0  0 0 | * * * * 4 * * *
..(..) .o(.o)3.x(.o)&#x  ♦ 0  3 0 1 | 0  0  0  3  0  3  0 | 0  0  0 0 0 1  0  3  0 0 | * * * * * 4 * *
.x(oq) ..(..) .x(qo)&#x  ♦ 0  4 2 2 | 0  0  2  2  4  4  4 | 0  0  0 0 1 0  2  2  4 1 | * * * * * * 6 *
..(oq)3..(oo)3..(qo)&#zx ♦ 0  0 4 4 | 0  0  0  0  0  0 12 | 0  0  0 0 0 0  0  0  0 6 | * * * * * * * 1

ooo3oxo4sox&#xt   → height(1,2) = sqrt(5/8) = 0.790569
                    height(2,3) = sqrt[sqrt(2)-3/4] = 0.814993
(tet || co || cube)

demiA( o..3o..4o..    ) | 4  * * * ♦ 3  3  0  0  0  0  0 | 3  6  3 0 0 0  0  0  0 0 | 1 3 3 1 0 0 0 0
both(  .o.3.o.4.o.    ) | * 12 * * | 0  1  2  2  1  1  0 | 0  2  2 1 2 1  2  2  1 0 | 0 1 2 1 1 1 2 0
demiA( ..o3..o4..o    ) | *  * 4 * | 0  0  0  0  3  0  3 | 0  0  0 0 0 0  3  0  3 3 | 0 0 0 0 1 0 3 1
demiB( ..o3..o4..o    ) | *  * * 4 | 0  0  0  0  0  3  3 | 0  0  0 0 0 0  0  3  3 3 | 0 0 0 0 0 1 3 1
------------------------+----------+---------------------+--------------------------+----------------
       ... o..4s..      | 2  0 0 0 | 6  *  *  *  *  *  * | 2  2  0 0 0 0  0  0  0 0 | 1 2 1 0 0 0 0 0
demiA( oo.3oo.4oo.&#x ) | 1  1 0 0 | * 12  *  *  *  *  * | 0  2  2 0 0 0  0  0  0 0 | 0 1 2 1 0 0 0 0
demiA( ... .x. ...    ) | 0  2 0 0 | *  * 12  *  *  *  * | 0  1  0 1 1 0  1  0  0 0 | 0 1 1 0 1 0 1 0
demiB( ... .x. ...    ) | 0  2 0 0 | *  *  * 12  *  *  * | 0  0  1 0 1 1  0  1  0 0 | 0 0 1 1 0 1 1 0
demiA( .oo3.oo4.oo&#x ) | 0  1 1 0 | *  *  *  * 12  *  * | 0  0  0 0 0 0  2  0  1 0 | 0 0 0 0 1 0 2 0
demiB( .oo3.oo4.oo&#x ) | 0  1 0 1 | *  *  *  *  * 12  * | 0  0  0 0 0 0  0  2  1 0 | 0 0 0 0 0 1 2 0
both(  ... ... ..x    ) | 0  0 1 1 | *  *  *  *  *  * 12 | 0  0  0 0 0 0  0  0  1 2 | 0 0 0 0 0 0 2 1
------------------------+----------+---------------------+--------------------------+----------------
sefaA( o..3o..4s..    ) | 3  0 0 0 | 3  0  0  0  0  0  0 | 4  *  * * * *  *  *  * * | 1 1 0 0 0 0 0 0
sefaA( ... ox.4so.&#x ) | 2  2 0 0 | 1  2  1  0  0  0  0 | * 12  * * * *  *  *  * * | 0 1 1 0 0 0 0 0
demiA( ... ox. ...&#x ) | 1  2 0 0 | 0  2  0  1  0  0  0 | *  * 12 * * *  *  *  * * | 0 0 1 1 0 0 0 0
demiA( .o.3.x. ...    ) | 0  3 0 0 | 0  0  3  0  0  0  0 | *  *  * 4 * *  *  *  * * | 0 1 0 0 1 0 0 0
both(  ... .x.4.o.    ) | 0  4 0 0 | 0  0  2  2  0  0  0 | *  *  * * 6 *  *  *  * * | 0 0 1 0 0 0 1 0
demiB( .o.3.x. ...    ) | 0  3 0 0 | 0  0  0  3  0  0  0 | *  *  * * * 4  *  *  * * | 0 0 0 1 0 1 0 0
demiA( ... .xo ...&#x ) | 0  2 1 0 | 0  0  1  0  2  0  0 | *  *  * * * * 12  *  * * | 0 0 0 0 1 0 1 0
demiB( ... .xo ...&#x ) | 0  2 0 1 | 0  0  0  1  0  2  0 | *  *  * * * *  * 12  * * | 0 0 0 0 0 1 1 0
both(  ... ... .ox&#x ) | 0  1 1 1 | 0  0  0  0  1  1  1 | *  *  * * * *  *  * 12 * | 0 0 0 0 0 0 2 0
both(  ... ..o4..x    ) | 0  0 2 2 | 0  0  0  0  0  0  4 | *  *  * * * *  *  *  * 6 | 0 0 0 0 0 0 1 1
------------------------+----------+---------------------+--------------------------+----------------
       o..3o..4s..      ♦ 4  0 0 0 | 6  0  0  0  0  0  0 | 4  0  0 0 0 0  0  0  0 0 | 1 * * * * * * *
sefaA( oo.3ox.4so.&#x ) ♦ 3  3 0 0 | 3  3  3  0  0  0  0 | 1  3  0 1 0 0  0  0  0 0 | * 4 * * * * * *
       ... ox.4so.&#x   ♦ 1  4 2 2 | 1  4  2  2  0  0  0 | 0  2  2 0 1 0  0  0  0 0 | * * 6 * * * * *
demiA( oo.3ox. ...&#x ) ♦ 1  3 0 0 | 0  3  0  3  0  0  0 | 0  0  3 0 0 1  0  0  0 0 | * * * 4 * * * *
demiA( .oo3.xo ...&#x ) ♦ 0  3 1 0 | 0  0  3  0  3  0  0 | 0  0  0 1 0 0  3  0  0 0 | * * * * 4 * * *
demiB( .oo3.xo ...&#x ) ♦ 0  3 0 1 | 0  0  0  3  0  3  0 | 0  0  0 0 0 1  0  3  0 0 | * * * * * 4 * *
both(  ... .xo4.ox&#x ) ♦ 0  4 2 2 | 0  0  2  2  4  4  4 | 0  0  0 0 1 0  2  2  4 1 | * * * * * * 6 *
both(  ..o3..o4..x    ) ♦ 0  0 4 4 | 0  0  0  0  0  0 12 | 0  0  0 0 0 0  0  0  0 6 | * * * * * * * 1

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