The icosahedral group I is the group of 60 rotational symmetries of a dodecahedron. A diagonal of the dodecahedron is a segment joining opposite vertices. There are 10 such diagonals. How many rotations of I are in the stabilizer of a diagonal? (You do not need to describe them, just figure out their number.) Justify your answer using group actions and the counting formula.
The icosahedral group I is the group of 60 rotational symmetries of a dodecahedron. A diagonal of the dodecahedron is a segment joining opposite vertices. There are 10 such diagonals. How many rotations of I are in the stabilizer of a diagonal? (You do not need to describe them, just figure out their number.) Justify your answer using group actions and the counting formula.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The icosahedral group I is the group of 60 rotational symmetries of a dodecahedron. A
diagonal of the dodecahedron is a segment joining opposite vertices. There are 10 such
diagonals. How many rotations of I are in the stabilizer of a diagonal? (You do not need
to describe them, just figure out their number.) Justify your answer using group actions
and the counting formula.
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