DuckieDai Euler Polyhedral Formula Python Program

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geometry · MIT License

Overview

Solve one missing vertex, edge, or face count from Euler's polyhedral formula.

Usage

Inputs

Exactly two known nonnegative whole-number counts for vertices, edges, and faces

Outputs

The remaining count from V - E + F = 2

Units: Counts are whole numbers.

Assumptions and limitations

Assumptions

The object satisfies Euler's polyhedral formula.

Constraints

Leave exactly one value blank in the TI program.

Known failures

Values that do not describe the intended polyhedron may produce a mathematically valid but inapplicable count.

Compatibility and review

Review status: Tested on a TI calculator
Tested on: TI-84 Plus CE Python; OS 5.8.3; Python App 5.8.3.0048; exact source owner-tested through TI Connect CE
What happened: Owner confirmed the supplied Euler formula program runs on the physical calculator.
Dependencies: No imports
Suggested calculator name: EULERPF — you can give it another valid, unique name when you transfer it
Desktop test cases: Not available for this interactive-only source

This exact source auto-launches an interactive calculator session, so compatibility evidence comes from the recorded physical-device review rather than an importable desktop fixture.

Browser preview

Try Euler's formula

This browser preview solves faces from vertices and edges. The TI program lets you leave any one of the three counts blank.

Simulation boundary: This preview uses a reviewed browser adapter. It does not execute the downloaded Python and does not prove TI-Python or calculator compatibility.

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Exact reviewed bytes

Source code

Download .py

View source below, copy it when JavaScript is available, or download the exact .py bytes.

"""DuckieDai Euler Polyhedron for TI-84 Plus CE Python."""


def duckiedai_intro(program_name, wait=True):
    """Show the reusable DuckieDai program opening."""
    title = program_name[:16]
    empty = 16 - len(title)
    left = empty // 2
    right = empty - left

    print("+----------------------+")
    print("|   " + " " * left + title + " " * right + "   |")
    print("|                      |")
    print("|       __             |")
    print("|   ___(o )>  quack!   |")
    print("|   \\ <_. )           |")
    print("|    `---'             |")
    print("|     by DuckieDai     |")
    print("+----------------------+")
    print("Loading...")

    if wait:
        input("Press enter to start ")
        print("\n" * 6)


def optional_count(prompt):
    """Return a nonnegative integer or None if blank."""
    while True:
        raw = input(prompt)

        if raw == "":
            return None

        try:
            value = int(raw)

            if value >= 0:
                return value

        except ValueError:
            pass

        print("Enter a whole number")
        print("or leave blank.")


def main():
    duckiedai_intro("EULER FORMULA")

    print("EULER POLYHEDRAL")
    print("FORMULA")
    print()
    print("V - E + F = 2")
    print()
    print("V = vertices")
    print("E = edges")
    print("F = faces")
    print()
    print("Enter known values.")
    print("Leave ONE blank")
    print("to solve for it.")
    print()

    V = optional_count("Vertices V: ")
    E = optional_count("Edges E: ")
    F = optional_count("Faces F: ")

    known = 0

    if V is not None:
        known += 1

    if E is not None:
        known += 1

    if F is not None:
        known += 1

    print()

    # ==========================================
    # SOLVE VERTICES
    #
    # V - E + F = 2
    # V = 2 + E - F
    # ==========================================

    if known == 2 and V is None:

        V = 2 + E - F

        print("Using:")
        print("V - E + F = 2")
        print()
        print("Rearranged:")
        print("V = 2 + E - F")
        print()
        print("ANSWER")
        print("Vertices = " + str(V))

    # ==========================================
    # SOLVE EDGES
    #
    # E = V + F - 2
    # ==========================================

    elif known == 2 and E is None:

        E = V + F - 2

        print("Using:")
        print("V - E + F = 2")
        print()
        print("Rearranged:")
        print("E = V + F - 2")
        print()
        print("ANSWER")
        print("Edges = " + str(E))

    # ==========================================
    # SOLVE FACES
    #
    # F = 2 - V + E
    # ==========================================

    elif known == 2 and F is None:

        F = 2 - V + E

        print("Using:")
        print("V - E + F = 2")
        print()
        print("Rearranged:")
        print("F = 2 - V + E")
        print()
        print("ANSWER")
        print("Faces = " + str(F))

    # ==========================================
    # VERIFY ALL THREE VALUES
    # ==========================================

    elif known == 3:

        result = V - E + F

        print("Checking:")
        print()
        print(str(V) + " - " +
              str(E) + " + " +
              str(F))
        print()
        print("Result = " + str(result))
        print()

        if result == 2:

            print("VALID")
            print()
            print("Euler formula")
            print("is satisfied.")

        else:

            print("NOT VALID")
            print()
            print("Expected result:")
            print("2")

    else:

        print("Need at least")
        print("two known values.")

    print()
    print("DuckieDai says: done!")


# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

"""DuckieDai Euler Polyhedron for TI-84 Plus CE Python."""
def duckiedai_intro(program_name, wait=True):
"""Show the reusable DuckieDai program opening."""
title = program_name[:16]
empty = 16 - len(title)
left = empty // 2
right = empty - left
print("+----------------------+")
print("| " + " " * left + title + " " * right + " |")
print("| |")
print("| __ |")
print("| ___(o )> quack! |")
print("| \\ <_. ) |")
print("| `---' |")
print("| by DuckieDai |")
print("+----------------------+")
print("Loading...")
if wait:
input("Press enter to start ")
print("\n" * 6)
def optional_count(prompt):
"""Return a nonnegative integer or None if blank."""
while True:
raw = input(prompt)
if raw == "":
return None
try:
value = int(raw)
if value >= 0:
return value
except ValueError:
pass
print("Enter a whole number")
print("or leave blank.")
def main():
duckiedai_intro("EULER FORMULA")
print("EULER POLYHEDRAL")
print("FORMULA")
print()
print("V - E + F = 2")
print()
print("V = vertices")
print("E = edges")
print("F = faces")
print()
print("Enter known values.")
print("Leave ONE blank")
print("to solve for it.")
print()
V = optional_count("Vertices V: ")
E = optional_count("Edges E: ")
F = optional_count("Faces F: ")
known = 0
if V is not None:
known += 1
if E is not None:
known += 1
if F is not None:
known += 1
print()
# ==========================================
# SOLVE VERTICES
#
# V - E + F = 2
# V = 2 + E - F
# ==========================================
if known == 2 and V is None:
V = 2 + E - F
print("Using:")
print("V - E + F = 2")
print()
print("Rearranged:")
print("V = 2 + E - F")
print()
print("ANSWER")
print("Vertices = " + str(V))
# ==========================================
# SOLVE EDGES
#
# E = V + F - 2
# ==========================================
elif known == 2 and E is None:
E = V + F - 2
print("Using:")
print("V - E + F = 2")
print()
print("Rearranged:")
print("E = V + F - 2")
print()
print("ANSWER")
print("Edges = " + str(E))
# ==========================================
# SOLVE FACES
#
# F = 2 - V + E
# ==========================================
elif known == 2 and F is None:
F = 2 - V + E
print("Using:")
print("V - E + F = 2")
print()
print("Rearranged:")
print("F = 2 - V + E")
print()
print("ANSWER")
print("Faces = " + str(F))
# ==========================================
# VERIFY ALL THREE VALUES
# ==========================================
elif known == 3:
result = V - E + F
print("Checking:")
print()
print(str(V) + " - " +
str(E) + " + " +
str(F))
print()
print("Result = " + str(result))
print()
if result == 2:
print("VALID")
print()
print("Euler formula")
print("is satisfied.")
else:
print("NOT VALID")
print()
print("Expected result:")
print("2")
else:
print("Need at least")
print("two known values.")
print()
print("DuckieDai says: done!")
# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

Filename: EULERPF.py
Size: 4037 bytes
SHA-256: ad1a878f3de1e5db1051e22de457d37604340cec90547b575d86362b18c238ce

Transfer and launch

Confirm that your calculator is the Python-capable model named above. Check that its OS and Python App versions match the reviewed record.
Download the .py source above and verify its SHA-256 digest if your computer provides that option.
Use TI Connect CE to send the Python file to a compatible calculator. EULERPF is a suggested name; you may choose another valid, unique calculator name.
Open the Python App, select the program, and check sample inputs before relying on other results.

Read the complete installation, launch, troubleshooting, and removal guide.

Availability does not mean a teacher, school, or exam permits this program. Follow the applicable rules.

Version history

1.0.0 — current version, published 2026-09-24. Download this reviewed version

Any source change requires a new immutable version and digest. Historical downloads remain available only while their review records remain valid.

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