Acronym | pex hex |
Name |
partially (mono-)expanded hex, partially contracted quawros |
Lace city in approx. ASCII-art |
o4o o4o o4o o4x o4x o4o o4o o4o |
x3o x3o o3o o3o o3x o3x | |
Dihedral angles | |
Face vector | 14, 42, 52, 24 |
Confer |
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Incidence matrix according to Dynkin symbol
oxxo3oooo4oooo&#xt → outer heights = 1/sqrt(2) = 0.707107 inner height = 1 (point || pseudo oct || pseudo oct || point) o...3o...4o... & | 2 * ♦ 6 0 0 | 12 0 0 | 8 0 .o..3.o..4.o.. & | * 12 | 1 4 1 | 4 4 4 | 4 4 ----------------------+------+---------+----------+----- oo..3oo..4oo..&#x & | 1 1 | 12 * * | 4 0 0 | 4 0 .x.. .... .... & | 0 2 | * 24 * | 1 2 1 | 2 2 .oo.3.oo.4.oo.&#x | 0 2 | * * 6 | 0 0 4 | 0 4 ----------------------+------+---------+----------+----- ox.. .... ....&#x & | 1 2 | 2 1 0 | 24 * * | 2 0 .x..3.o.. .... & | 0 3 | 0 3 0 | * 16 * | 1 1 .xx. .... ....&#x | 0 4 | 0 2 2 | * * 12 | 0 2 ----------------------+------+---------+----------+----- ox..3oo.. ....&#x & ♦ 1 3 | 3 3 0 | 3 1 0 | 16 * .xx.3.oo. ....&#x ♦ 0 6 | 0 6 3 | 0 2 3 | * 8
o(ox)o4o(oo)o x(wx)x&#xt → both heights = 1/sqrt(2) = 0.707107 (line || pseudo esquidpy || line) o(..).4o(..). o(..). & | 4 * * | 1 1 4 0 0 0 | 4 4 4 0 0 | 4 4 .(o.).4.(o.). .(o.). | * 2 * ♦ 0 2 0 4 0 0 | 8 0 0 4 0 | 8 0 .(.o).4.(.o). .(.o). | * * 8 | 0 0 2 1 2 1 | 2 4 2 2 4 | 4 4 ---------------------------+-------+--------------+-------------+----- .(..). .(..). x(..). & | 2 0 0 | 2 * * * * * | 0 0 4 0 0 | 0 4 o(o.).4o(o.). o(o.).&#x & | 1 1 0 | * 4 * * * * | 4 0 0 0 0 | 4 0 o(.o).4o(.o). o(.o).&#x & | 1 0 1 | * * 16 * * * | 1 2 1 0 0 | 2 2 .(oo).4.(oo). .(oo).&#x | 0 1 1 | * * * 8 * * | 2 0 0 2 0 | 4 0 .(.x). .(..). .(..). | 0 0 2 | * * * * 8 * | 0 2 0 1 1 | 2 2 .(..). .(..). .(.x). | 0 0 2 | * * * * * 4 | 0 0 2 0 2 | 0 4 ---------------------------+-------+--------------+-------------+----- o(oo).4o(oo). o(oo).&#x & | 1 1 1 | 0 1 1 1 0 0 | 16 * * * * | 2 0 o(.x). .(..). .(..).&#x & | 1 0 2 | 0 0 2 0 1 0 | * 16 * * * | 1 1 .(..). .(..). x(.x).&#x & | 2 0 2 | 1 0 2 0 0 1 | * * 8 * * | 0 2 .(ox). .(..). .(..).&#x | 0 1 2 | 0 0 0 2 1 0 | * * * 8 * | 2 0 .(.x). .(..). .(.x). | 0 0 4 | 0 0 0 0 2 2 | * * * * 4 | 0 2 ---------------------------+-------+--------------+-------------+----- o(ox). .(..). .(..).&#x & ♦ 1 1 2 | 0 1 2 2 1 0 | 2 1 0 1 0 | 16 * o(.x). .(..). x(.x).&#x & ♦ 2 0 4 | 1 0 4 0 2 2 | 0 2 2 0 1 | * 8
o(qoo)o o(oqo)o x(xxw)x&#xt → both heights = 1/sqrt(2) = 0.707107 (line || pseudo esquidpy || line) o(...). o(...). o(...). | 2 * * * * | 1 2 2 1 0 0 0 0 0 0 0 0 0 | 2 2 4 2 2 0 0 0 0 0 0 0 | 4 4 0 0 .(o..). .(o..). .(o..). | * 4 * * * | 0 1 0 0 1 2 1 1 0 0 0 0 0 | 1 0 2 1 0 2 2 1 2 1 0 0 | 2 2 2 2 .(.o.). .(.o.). .(.o.). | * * 4 * * | 0 0 1 0 0 2 0 0 1 1 1 0 0 | 0 1 2 0 1 2 2 0 2 0 1 1 | 2 2 2 2 .(..o). .(..o). .(..o). | * * * 2 * ♦ 0 0 0 1 0 0 2 0 0 2 0 1 0 | 0 0 0 2 2 0 4 0 0 2 0 2 | 0 4 0 4 .(...)o .(...)o .(...)o | * * * * 2 | 0 0 0 0 0 0 0 2 0 0 2 1 1 | 0 0 0 0 0 0 0 2 4 2 2 2 | 0 0 4 4 ---------------------------+-----------+---------------------------+-------------------------+-------- .(...). .(...). x(...). | 2 0 0 0 0 | 1 * * * * * * * * * * * * | 2 2 0 0 0 0 0 0 0 0 0 0 | 4 0 0 0 o(o..). o(o..). o(o..).&#x | 1 1 0 0 0 | * 4 * * * * * * * * * * * | 1 0 2 1 0 0 0 0 0 0 0 0 | 2 2 0 0 o(.o.). o(.o.). o(.o.).&#x | 1 0 1 0 0 | * * 4 * * * * * * * * * * | 0 1 2 0 1 0 0 0 0 0 0 0 | 2 2 0 0 o(..o). o(..o). o(..o).&#x | 1 0 0 1 0 | * * * 2 * * * * * * * * * | 0 0 0 2 2 0 0 0 0 0 0 0 | 0 4 0 0 .(...). .(...). .(x..). | 0 2 0 0 0 | * * * * 2 * * * * * * * * | 1 0 0 0 0 2 0 1 0 0 0 0 | 2 0 2 0 .(oo.). .(oo.). .(oo.).&#x | 0 1 1 0 0 | * * * * * 8 * * * * * * * | 0 0 1 0 0 1 1 0 1 0 0 0 | 1 1 1 1 .(o.o). .(o.o). .(o.o).&#x | 0 1 0 1 0 | * * * * * * 4 * * * * * * | 0 0 0 1 0 0 2 0 0 1 0 0 | 0 2 0 2 .(o..)o .(o..)o .(o..)o&#x | 0 1 0 0 1 | * * * * * * * 4 * * * * * | 0 0 0 0 0 0 0 1 2 1 0 0 | 0 0 2 2 .(...). .(...). .(.x.). | 0 0 2 0 0 | * * * * * * * * 2 * * * * | 0 1 0 0 0 2 0 0 0 0 1 0 | 2 0 2 0 .(.oo). .(.oo). .(.oo).&#x | 0 0 1 1 0 | * * * * * * * * * 4 * * * | 0 0 0 0 1 0 2 0 0 0 0 1 | 0 2 0 2 .(.o.)o .(.o.)o .(.o.)o&#x | 0 0 1 0 1 | * * * * * * * * * * 4 * * | 0 0 0 0 0 0 0 0 2 0 1 1 | 0 0 2 2 .(..o)o .(..o)o .(..o)o&#x | 0 0 0 1 1 | * * * * * * * * * * * 2 * | 0 0 0 0 0 0 0 0 0 2 0 2 | 0 0 0 4 .(...). .(...). .(...)x | 0 0 0 0 2 | * * * * * * * * * * * * 1 | 0 0 0 0 0 0 0 2 0 0 2 0 | 0 0 4 0 ---------------------------+-----------+---------------------------+-------------------------+-------- .(...). .(...). x(x..).&#x | 2 2 0 0 0 | 1 2 0 0 1 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * * * | 2 0 0 0 .(...). .(...). x(.x.).&#x | 2 0 2 0 0 | 1 0 2 0 0 0 0 0 1 0 0 0 0 | * 2 * * * * * * * * * * | 2 0 0 0 o(oo.). o(oo.). o(oo.).&#x | 1 1 1 0 0 | 0 1 1 0 0 1 0 0 0 0 0 0 0 | * * 8 * * * * * * * * * | 1 1 0 0 o(o.o). o(o.o). o(o.o).&#x | 1 1 0 1 0 | 0 1 0 1 0 0 1 0 0 0 0 0 0 | * * * 4 * * * * * * * * | 0 2 0 0 o(.oo). o(.oo). o(.oo).&#x | 1 0 1 1 0 | 0 0 1 1 0 0 0 0 0 1 0 0 0 | * * * * 4 * * * * * * * | 0 2 0 0 .(...). .(...). .(xx.).&#x | 0 2 2 0 0 | 0 0 0 0 1 2 0 0 1 0 0 0 0 | * * * * * 4 * * * * * * | 1 0 1 0 .(ooo). .(ooo). .(ooo).&#x | 0 1 1 1 0 | 0 0 0 0 0 1 1 0 0 1 0 0 0 | * * * * * * 8 * * * * * | 0 1 0 1 .(...). .(...). .(x..)x&#x | 0 2 0 0 2 | 0 0 0 0 1 0 0 2 0 0 0 0 1 | * * * * * * * 2 * * * * | 0 0 2 0 .(oo.)o .(oo.)o .(oo.)o&#x | 0 1 1 0 1 | 0 0 0 0 0 1 0 1 0 0 1 0 0 | * * * * * * * * 8 * * * | 0 0 1 1 .(o.o)o .(o.o)o .(o.o)o&#x | 0 1 0 1 1 | 0 0 0 0 0 0 1 1 0 0 0 1 0 | * * * * * * * * * 4 * * | 0 0 0 2 .(...). .(...). .(.x.)x&#x | 0 0 2 0 2 | 0 0 0 0 0 0 0 0 1 0 2 0 1 | * * * * * * * * * * 2 * | 0 0 2 0 .(.oo)o .(.oo)o .(.oo)o&#x | 0 0 1 1 1 | 0 0 0 0 0 0 0 0 0 1 1 1 0 | * * * * * * * * * * * 4 | 0 0 0 2 ---------------------------+-----------+---------------------------+-------------------------+-------- .(...). .(...). x(xx.).&#x ♦ 2 2 2 0 0 | 1 2 2 0 1 2 0 0 1 0 0 0 0 | 1 1 2 0 0 1 0 0 0 0 0 0 | 4 * * * o(ooo). o(ooo). o(ooo).&#x ♦ 1 1 1 1 0 | 0 1 1 1 0 1 1 0 0 1 0 0 0 | 0 0 1 1 1 0 1 0 0 0 0 0 | * 8 * * .(...). .(...). .(xx.)x&#x ♦ 0 2 2 0 2 | 0 0 0 0 1 2 0 2 1 0 2 0 1 | 0 0 0 0 0 1 0 1 2 0 1 0 | * * 4 * .(ooo)o .(ooo)o .(ooo)o&#x ♦ 0 1 1 1 1 | 0 0 0 0 0 1 1 1 0 1 1 1 0 | 0 0 0 0 0 0 1 0 1 1 0 1 | * * * 8
oox3xoo xwx&#xt → both heights = 1/sqrt(6) = 0.408248 (trip || pseudo w-line || inv trip) o..3o.. o.. & | 12 * | 2 1 1 2 | 1 2 2 3 2 2 | 1 1 3 3 .o.3.o. .o. | * 2 ♦ 0 0 6 0 | 0 0 6 0 0 6 | 0 2 0 6 ------------------+------+------------+----------------+--------- ... x.. ... & | 2 0 | 12 * * * | 1 1 1 1 0 0 | 1 1 1 1 ... ... x.. & | 2 0 | * 6 * * | 0 2 0 0 2 0 | 1 0 3 0 oo.3oo. oo.&#x & | 1 1 | * * 12 * | 0 0 2 0 0 2 | 0 1 0 3 o.o3o.o o.o&#x | 2 0 | * * * 12 | 0 0 0 2 1 1 | 0 0 2 2 ------------------+------+------------+----------------+--------- o..3x.. ... & | 3 0 | 3 0 0 0 | 4 * * * * * | 1 1 0 0 ... x.. x.. & | 4 0 | 2 2 0 0 | * 6 * * * * | 1 0 1 0 ... xo. ...&#x & | 2 1 | 1 0 2 0 | * * 12 * * * | 0 1 0 1 o.x ... ...&#x & | 3 0 | 1 0 0 2 | * * * 12 * * | 0 0 1 1 ... ... x.x&#x | 4 0 | 0 2 0 2 | * * * * 6 * | 0 0 2 0 ooo3ooo ooo&#x | 2 1 | 0 0 2 1 | * * * * * 12 | 0 0 0 2 ------------------+------+------------+----------------+--------- o..3x.. x.. & ♦ 6 0 | 6 3 0 0 | 2 3 0 0 0 0 | 2 * * * oo.3xo. ...&#x & ♦ 3 1 | 3 0 3 0 | 1 0 3 0 0 0 | * 4 * * o.x ... x.x&#x & ♦ 6 0 | 2 3 0 4 | 0 1 0 2 2 0 | * * 6 * oox ... ...&#x & ♦ 3 1 | 1 0 3 2 | 0 0 1 1 0 2 | * * * 12
wx ox3oo4oo&#zx → height = 0 (tegum sum of w-line and ope) o. o.3o.4o. | 2 * ♦ 6 0 0 | 12 0 0 | 8 0 .o .o3.o4.o | * 12 | 1 1 4 | 4 4 4 | 4 4 ----------------+------+---------+----------+----- oo oo3oo4oo&#x | 1 1 | 12 * * | 4 0 0 | 4 0 .x .. .. .. | 0 2 | * 6 * | 0 4 0 | 0 4 .. .x .. .. | 0 2 | * * 24 | 1 1 2 | 2 2 ----------------+------+---------+----------+----- .. ox .. ..&#x | 1 2 | 2 0 1 | 24 * * | 2 0 .x .x .. .. | 0 4 | 0 2 2 | * 12 * | 0 2 .. .x3.o .. | 0 3 | 0 0 3 | * * 16 | 1 1 ----------------+------+---------+----------+----- .. ox3oo ..&#x ♦ 1 3 | 3 0 3 | 3 0 1 | 16 * .x .x3.o .. ♦ 0 6 | 0 3 6 | 0 3 2 | * 8
wxxx oqoo ooqo oooq&#zx → height = 0 (tegum sum of w-line and 3 ortho (q,x)-{4}) o... o... o... o... | 2 * * * ♦ 2 2 2 0 0 0 0 0 0 | 4 4 4 0 0 0 0 | 8 0 .o.. .o.. .o.. .o.. | * 4 * * | 1 0 0 1 2 2 0 0 0 | 2 2 0 2 2 4 0 | 4 4 ..o. ..o. ..o. ..o. | * * 4 * | 0 1 0 0 2 0 1 2 0 | 2 0 2 2 0 4 2 | 4 4 ...o ...o ...o ...o | * * * 4 | 0 0 1 0 0 2 0 2 1 | 0 2 2 0 2 4 2 | 4 4 ------------------------+---------+-------------------+----------------+----- oo.. oo.. oo.. oo..&#x | 1 1 0 0 | 4 * * * * * * * * | 2 2 0 0 0 0 0 | 4 0 o.o. o.o. o.o. o.o.&#x | 1 0 1 0 | * 4 * * * * * * * | 2 0 2 0 0 0 0 | 4 0 o..o o..o o..o o..o&#x | 1 0 0 1 | * * 4 * * * * * * | 0 2 2 0 0 0 0 | 4 0 .x.. .... .... .... | 0 2 0 0 | * * * 2 * * * * * | 0 0 0 2 2 0 0 | 0 4 .oo. .oo. .oo. .oo.&#x | 0 1 1 0 | * * * * 8 * * * * | 1 0 0 1 0 2 0 | 2 2 .o.o .o.o .o.o .o.o&#x | 0 1 0 1 | * * * * * 8 * * * | 0 1 0 0 1 2 0 | 2 2 ..x. .... .... .... | 0 0 2 0 | * * * * * * 2 * * | 0 0 0 2 0 0 2 | 0 4 ..oo ..oo ..oo ..oo&#x | 0 0 1 1 | * * * * * * * 8 * | 0 0 1 0 0 2 1 | 2 2 ...x .... .... .... | 0 0 0 2 | * * * * * * * * 2 | 0 0 0 0 2 0 2 | 0 4 ------------------------+---------+-------------------+----------------+----- ooo. ooo. ooo. ooo.&#x | 1 1 1 0 | 1 1 0 0 1 0 0 0 0 | 8 * * * * * * | 2 0 oo.o oo.o oo.o oo.o&#x | 1 1 0 1 | 1 0 1 0 0 1 0 0 0 | * 8 * * * * * | 2 0 o.oo o.oo o.oo o.oo&#x | 1 0 1 1 | 0 1 1 0 0 0 0 1 0 | * * 8 * * * * | 2 0 .xx. .... .... ....&#x | 0 2 2 0 | 0 0 0 1 2 0 1 0 0 | * * * 4 * * * | 0 2 .x.x .... .... ....&#x | 0 2 0 2 | 0 0 0 1 0 2 0 0 1 | * * * * 4 * * | 0 2 .ooo .ooo .ooo .ooo&#x | 0 1 1 1 | 0 0 0 0 1 1 0 1 0 | * * * * * 16 * | 1 1 ..xx .... .... ....&#x | 0 0 2 2 | 0 0 0 0 0 0 1 2 1 | * * * * * * 4 | 0 2 ------------------------+---------+-------------------+----------------+----- oooo oooo oooo oooo&#x ♦ 1 1 1 1 | 1 1 1 0 1 1 0 1 0 | 1 1 1 0 0 1 0 | 16 * .xxx .... .... ....&#x ♦ 0 2 2 2 | 0 0 0 1 2 2 1 2 1 | 0 0 0 1 1 2 1 | * 8
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