Acronym | squapt |
Name |
(line-)square-antiprismatic tegum, square-antiprismatic bipyramid, square-pyramidal antiprism |
Lace city in approx. ASCII-art |
o4o x4o o4x o4o |
Dihedral angles |
|
Face vector | 10, 32, 42, 20 |
Confer |
|
Incidence matrix according to Dynkin symbol
pt || pseudo squap || pt → both heights = sqrt[(4-sqrt(2))/8] = 0.568527 1 * * | 8 0 0 0 | 8 8 0 0 0 0 | 2 8 0 0 verf: squap * 8 * | 1 2 2 1 | 2 2 1 3 2 2 | 1 3 1 3 * * 1 | 0 0 0 8 | 0 0 0 0 8 8 | 0 0 2 8 verf: squap ------+---------+-------------+-------- 1 1 0 | 8 * * * | 2 2 0 0 0 0 | 1 3 0 0 0 2 0 | * 8 * * | 1 0 1 1 1 0 | 1 1 1 1 0 2 0 | * * 8 * | 0 1 0 2 0 1 | 0 2 0 2 0 1 1 | * * * 8 | 0 0 0 0 2 2 | 0 0 1 3 ------+---------+-------------+-------- 1 2 0 | 2 1 0 0 | 8 * * * * * | 1 1 0 0 1 2 0 | 2 0 1 0 | * 8 * * * * | 0 2 0 0 0 4 0 | 0 4 0 0 | * * 2 * * * | 1 0 1 0 {4} 0 3 0 | 0 1 2 0 | * * * 8 * * | 0 1 0 1 0 2 1 | 0 1 0 2 | * * * * 8 * | 0 0 1 1 0 2 1 | 0 0 1 2 | * * * * * 8 | 0 0 0 2 ------+---------+-------------+-------- 1 4 0 | 4 4 0 0 | 4 0 1 0 0 0 | 2 * * * squippy 1 3 0 | 3 1 2 0 | 1 2 0 1 0 0 | * 8 * * tet 0 4 1 | 0 4 0 4 | 0 0 1 0 4 0 | * * 2 * squippy 0 3 1 | 0 1 2 3 | 0 0 0 1 1 2 | * * * 8 tet
ox4oo&#x || oo4xo&#x → height = sqrt[sqrt(8)-1]/2 = 0.676097 squippy || inv gyro squippy o.4o. .. .. | 1 * * * ♦ 4 4 0 0 0 0 0 | 4 4 8 0 0 0 0 0 0 0 | 1 1 4 4 0 0 0 0 .o4.o .. .. | * 4 * * | 1 0 2 2 1 0 0 | 2 0 2 1 2 2 1 2 0 0 | 1 0 2 1 1 2 1 0 .. .. o.4o. | * * 4 * | 0 1 0 2 0 2 1 | 0 2 2 0 1 0 2 2 1 2 | 0 1 1 2 0 1 2 1 .. .. .o4.o | * * * 1 ♦ 0 0 0 0 4 0 4 | 0 0 0 0 0 4 0 8 0 4 | 0 0 0 0 1 4 4 1 --------------------+---------+---------------+---------------------+---------------- oo4oo&#x .. .. | 1 1 0 0 | 4 * * * * * * | 2 0 2 0 0 0 0 0 0 0 | 1 0 2 1 0 0 0 0 o.4o. || o.4o. | 1 0 1 0 | * 4 * * * * * | 0 2 2 0 0 0 0 0 0 0 | 0 1 1 2 0 0 0 0 .x .. .. .. | 0 2 0 0 | * * 4 * * * * | 1 0 0 1 1 1 0 0 0 0 | 1 0 1 0 1 1 0 0 .o4.o || o.4o. | 0 1 1 0 | * * * 8 * * * | 0 0 1 0 1 0 1 1 0 0 | 0 0 1 1 0 1 1 0 .o4.o || .o4.o | 0 1 0 1 | * * * * 4 * * | 0 0 0 0 0 2 0 2 0 0 | 0 0 0 0 1 2 1 0 .. .. .. x. | 0 0 2 0 | * * * * * 4 * | 0 1 0 0 0 0 1 0 0 2 | 0 1 0 1 0 0 1 1 .. .. oo4oo&#x | 0 0 1 1 | * * * * * * 4 | 0 0 0 0 0 0 0 2 1 1 | 0 0 0 0 0 1 2 1 --------------------+---------+---------------+---------------------+---------------- ox ..&#x .. .. | 1 2 0 0 | 2 0 1 0 0 0 0 | 4 * * * * * * * * * | 1 0 1 0 0 0 0 0 o.4o. || .. x. | 1 0 2 0 | 0 2 0 0 0 1 0 | * 4 * * * * * * * * | 0 1 0 1 0 0 0 0 oo4oo&#x || o.4o. | 1 1 1 0 | 1 1 0 1 0 0 0 | * * 8 * * * * * * * | 0 0 1 1 0 0 0 0 .x4.o .. .. | 0 4 0 0 | 0 0 4 0 0 0 0 | * * * 1 * * * * * * | 1 0 0 0 1 0 0 0 .x .. || o.4o. | 0 2 1 0 | 0 0 1 2 0 0 0 | * * * * 4 * * * * * | 0 0 1 0 0 1 0 0 .x .. || .o4.o | 0 2 0 1 | 0 0 1 0 2 0 0 | * * * * * 4 * * * * | 0 0 0 0 1 1 0 0 .o4.o || .. x. | 0 1 2 0 | 0 0 0 2 0 1 0 | * * * * * * 4 * * * | 0 0 0 1 0 0 1 0 .o4.o || oo4oo&#x | 0 1 1 1 | 0 0 0 1 1 0 1 | * * * * * * * 8 * * | 0 0 0 0 0 1 1 0 .. .. o.4x. | 0 0 4 0 | 0 0 0 0 0 0 4 | * * * * * * * * 1 * | 0 1 0 0 0 0 0 1 .. .. .. xo&#x | 0 0 2 1 | 0 0 0 0 0 2 1 | * * * * * * * * * 4 | 0 0 0 0 0 0 1 1 --------------------+---------+---------------+---------------------+---------------- ox4oo&#x .. .. ♦ 1 4 0 0 | 4 0 4 0 0 0 0 | 4 0 0 1 0 0 0 0 0 0 | 1 * * * * * * * o.4o. || o.4x. ♦ 1 0 4 0 | 0 4 0 0 0 4 0 | 0 4 0 0 0 0 0 0 1 0 | * 1 * * * * * * ox ..&#x || o.4o. ♦ 1 2 1 0 | 2 1 1 2 0 0 0 | 1 0 2 0 1 0 0 0 0 0 | * * 4 * * * * * oo4oo&#x || .. x. ♦ 1 1 2 0 | 1 2 0 2 0 1 0 | 0 1 2 0 0 0 1 0 0 0 | * * * 4 * * * * .x4.o || .o4.o ♦ 0 4 0 1 | 0 0 4 0 4 0 0 | 0 0 0 1 0 4 0 0 0 0 | * * * * 1 * * * .x .. || oo4oo&#x ♦ 0 2 1 1 | 0 0 1 2 2 0 1 | 0 0 0 0 1 1 0 2 0 0 | * * * * * 4 * * . o4.o || .. xo&#x ♦ 0 1 2 1 | 0 0 0 2 1 1 2 | 0 0 0 0 0 0 1 2 0 1 | * * * * * * 4 * .. .. oo4xo&#x ♦ 0 0 4 1 | 0 0 0 0 0 4 4 | 0 0 0 0 0 0 0 0 1 4 | * * * * * * * 1
oxoo4ooox&#xr → all heights = 1/sqrt(2) = 0.707107 (pt || pseudo ({4} || dual {4}) || pt) o...4o... | 1 * * * ♦ 4 4 0 0 0 0 0 | 4 8 4 0 0 0 0 0 0 0 | 1 1 4 4 0 0 0 0 .o..4.o.. | * 4 * * | 1 0 2 1 2 0 0 | 2 2 0 1 2 2 1 2 0 0 | 1 0 2 1 1 2 1 0 ..o.4..o. | * * 1 * ♦ 0 0 0 4 0 4 0 | 0 0 0 0 4 0 0 8 4 0 | 0 0 0 0 1 4 4 1 ...o4...o | * * * 4 | 0 1 0 0 2 1 2 | 0 2 2 0 0 1 2 2 2 1 | 0 1 1 2 0 1 2 1 -------------+---------+---------------+---------------------+---------------- oo..4oo..&#x | 1 1 0 0 | 4 * * * * * * | 2 2 0 0 0 0 0 0 0 0 | 1 0 2 1 0 0 0 0 o..o4o..o&#x | 1 0 0 1 | * 4 * * * * * | 0 2 2 0 0 0 0 0 0 0 | 0 1 1 2 0 0 0 0 .x.. .... | 0 2 0 0 | * * 4 * * * * | 1 0 0 1 1 1 0 0 0 0 | 1 0 1 0 1 1 0 0 .oo.4.oo.&#x | 0 1 1 0 | * * * 4 * * * | 0 0 0 0 2 0 0 2 0 0 | 0 0 0 0 1 2 1 0 .o.o4.o.o&#x | 0 1 0 1 | * * * * 8 * * | 0 1 0 0 0 1 1 1 0 0 | 0 0 1 1 0 1 1 0 ..oo4..oo&#x | 0 0 1 1 | * * * * * 4 * | 0 0 0 0 0 0 0 2 2 0 | 0 0 0 0 0 1 2 1 .... ...x | 0 0 0 2 | * * * * * * 4 | 0 0 1 0 0 0 1 0 1 1 | 0 1 0 1 0 0 1 1 -------------+---------+---------------+---------------------+---------------- ox.. ....&#x | 1 2 0 0 | 2 0 1 0 0 0 0 | 4 * * * * * * * * * | 1 0 1 0 0 0 0 0 oo.o4oo.o&#x | 1 1 0 1 | 1 1 0 0 1 0 0 | * 8 * * * * * * * * | 0 0 1 1 0 0 0 0 .... o..x&#x | 1 0 0 2 | 0 2 0 0 0 0 1 | * * 4 * * * * * * * | 0 1 0 1 0 0 0 0 .x..4.o.. | 0 4 0 0 | 0 0 4 0 0 0 0 | * * * 1 * * * * * * | 1 0 0 0 1 0 0 0 .xo. ....&#x | 0 2 1 0 | 0 0 1 2 0 0 0 | * * * * 4 * * * * * | 0 0 0 0 1 1 0 0 .x.o ....&#x | 0 2 0 1 | 0 0 1 0 2 0 0 | * * * * * 4 * * * * | 0 0 1 0 0 1 0 0 .... .o.x&#x | 0 1 0 2 | 0 0 0 0 2 0 1 | * * * * * * 4 * * * | 0 0 0 1 0 0 1 0 .ooo4.ooo&#x | 0 1 1 1 | 0 0 0 1 1 1 0 | * * * * * * * 8 * * | 0 0 0 0 0 1 1 0 .... ..ox&#x | 0 0 1 2 | 0 0 0 0 0 2 1 | * * * * * * * * 4 * | 0 0 0 0 0 0 1 1 ...o4...x | 0 0 0 4 | 0 0 0 0 0 0 4 | * * * * * * * * * 1 | 0 1 0 0 0 0 0 1 -------------+---------+---------------+---------------------+---------------- ox..4oo..&#x ♦ 1 4 0 0 | 4 0 4 0 0 0 0 | 4 0 0 1 0 0 0 0 0 0 | 1 * * * * * * * o..o4o..x&#x ♦ 1 0 0 4 | 0 4 0 0 0 0 4 | 0 0 4 0 0 0 0 0 0 1 | * 1 * * * * * * ox.o ....&#x ♦ 1 2 0 1 | 2 1 1 0 2 0 0 | 1 2 0 0 0 1 0 0 0 0 | * * 4 * * * * * .... oo.x&#x ♦ 1 1 0 2 | 1 2 0 0 2 0 1 | 0 2 1 0 0 0 1 0 0 0 | * * * 4 * * * * .xo.4.oo.&#x ♦ 0 4 1 0 | 0 0 4 4 0 0 0 | 0 0 0 1 4 0 0 0 0 0 | * * * * 1 * * * .xoo ....&#x ♦ 0 2 1 1 | 0 0 1 2 2 1 0 | 0 0 0 0 1 1 0 2 0 0 | * * * * * 4 * * .... .oox&#x ♦ 0 1 1 2 | 0 0 0 1 2 2 1 | 0 0 0 0 0 0 1 2 1 0 | * * * * * * 4 * ..oo4..ox&#x ♦ 0 0 1 4 | 0 0 0 0 0 4 4 | 0 0 0 0 0 0 0 0 4 1 | * * * * * * * 1
xoo4oox oyo&#xt → both heights = 1/sqrt(sqrt(32)) = 0.420448 ({4} || perp y-line || dual {4}) y = sqrt[(4-sqrt(2))/2] = 1.137055 o..4o.. o.. | 4 * * | 2 2 2 0 0 | 1 4 2 1 4 0 0 | 2 4 2 0 .o.4.o. .o. | * 2 * ♦ 0 4 0 4 0 | 0 4 0 0 8 4 0 | 1 4 4 1 ..o4..o ..o | * * 4 | 0 0 2 2 2 | 0 0 1 2 4 4 1 | 0 2 4 2 ----------------+-------+-----------+----------------+-------- x.. ... ... | 2 0 0 | 4 * * * * | 1 2 1 0 0 0 0 | 2 2 0 0 oo.4oo. oo.&#x | 1 1 0 | * 8 * * * | 0 2 0 0 2 0 0 | 1 2 1 0 o.o4o.o o.o&#x | 1 0 1 | * * 8 * * | 0 0 1 1 2 0 0 | 0 2 2 0 .oo4.oo .oo&#x | 0 1 1 | * * * 8 * | 0 0 0 0 2 2 0 | 0 1 2 1 ... ..x ... | 0 0 2 | * * * * 4 | 0 0 0 1 0 2 1 | 0 0 2 2 ----------------+-------+-----------+----------------+-------- x..4o.. ... | 4 0 0 | 4 0 0 0 0 | 1 * * * * * * | 2 0 0 0 xo. ... ...&#x | 2 1 0 | 1 2 0 0 0 | * 8 * * * * * | 1 1 0 0 x.o ... ...&#x | 2 0 1 | 1 0 2 0 0 | * * 4 * * * * | 0 2 0 0 ... o.x ...&#x | 1 0 2 | 0 0 2 0 1 | * * * 4 * * * | 0 0 2 0 ooo4ooo ooo&#xt | 1 1 1 | 0 1 1 1 0 | * * * * 16 * * | 0 1 1 0 ... .ox ...&#x | 0 1 2 | 0 0 0 2 1 | * * * * * 8 * | 0 0 1 1 ..o4..x ... | 0 0 4 | 0 0 0 0 4 | * * * * * * 1 | 0 0 0 2 ----------------+-------+-----------+----------------+-------- xo.4oo. ...&#x ♦ 4 1 0 | 4 4 0 0 0 | 1 4 0 0 0 0 0 | 2 * * * xoo ... ...&#xt ♦ 2 1 1 | 1 2 2 1 0 | 0 1 1 0 2 0 0 | * 8 * * ... oox ...&#xt ♦ 1 1 2 | 0 1 2 2 1 | 0 0 0 1 2 1 0 | * * 8 * .oo4.ox ...&#x ♦ 0 1 4 | 0 0 0 4 4 | 0 0 0 0 0 4 1 | * * * 2
yo os2os8os&#zx → height = 0 (tegum sum of y-line and perp squap) y = sqrt[(4-sqrt(2))/2] = 1.137055 (tegum product of y-line with squap) o. demi( o.2o.8o. ) | 2 * ♦ 8 0 0 | 8 8 0 0 | 2 8 .o demi( .o2.o8.o ) | * 8 | 2 2 2 | 4 4 1 3 | 2 6 -----------------------+-----+--------+-----------+----- oo demi( oo2oo8oo )&#x | 1 1 | 16 * * | 2 2 0 0 | 1 3 .. .s2.s .. | 0 2 | * 8 * | 2 0 0 2 | 0 4 .. sefa( .. .s8.s ) | 0 2 | * * 8 | 0 2 1 1 | 2 2 -----------------------+-----+--------+-----------+----- oo os2os .. &#x | 1 2 | 2 1 0 | 16 * * * | 0 2 oo sefa( .. os8os )&#x | 1 2 | 2 0 1 | * 16 * * | 1 1 .. .. .s8.s | 0 4 | 0 0 4 | * * 2 * | 2 0 .. sefa( .s2.s8.s ) | 0 3 | 0 2 1 | * * * 8 | 0 2 -----------------------+-----+--------+-----------+----- oo .. os8os &#x ♦ 1 4 | 4 0 4 | 0 4 1 0 | 4 * oo sefa( os2os8os )&#x ♦ 1 3 | 3 2 1 | 2 1 0 1 | * 16
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